>> BT 1 i /FormType 1 endstream << >> /F3 12.131 Tf Q 0.458 0 0 RG /Resources<< 1 i /BBox [0 0 15.59 16.44] /Resources<< Q Q 0 G 0 G /Meta1140 1158 0 R /F3 12.131 Tf /BBox [0 0 30.642 16.44] /Meta1595 Do Q /FormType 1 0 G /Subtype /Form Q 0.564 G /ProcSet[/PDF] q 1 i >> /Type /XObject /Matrix [1 0 0 1 0 0] 86.881 28.403 m /Font << >> /Type /Pages >> 0 g >> q 0 g /Matrix [1 0 0 1 0 0] /FormType 1 >> << 1 i endobj 0.564 G endstream /Resources<< 791 0 obj q /FormType 1 0.51 Tc q /Resources<< Q Q /Subtype /Form 1 i /Meta1163 1181 0 R ET endobj 505 0 obj 203.698 5.203 TD 1 i 0 G stream q 0.737 w ET stream /BBox [0 0 15.59 16.44] Q /F3 17 0 R /Matrix [1 0 0 1 0 0] stream /Type /XObject Q 0 G q /ProcSet[/PDF] Q /Resources<< /Font << q 0.564 G 0.738 Tc q 0.458 0 0 RG 1.007 0 0 1.007 411.035 453.193 cm /Meta930 Do /ProcSet[/PDF/Text] /Matrix [1 0 0 1 0 0] /Matrix [1 0 0 1 0 0] /Meta661 Do 1.005 0 0 1.007 102.382 721.194 cm stream 0.564 G Q 0.369 Tc Q /F4 24 0 R /Font << 0 G endobj >> 1 i >> q >> >> BT /Resources<< /ProcSet[/PDF] q /Resources<< 38.948 5.203 TD stream /Font << /ProcSet[/PDF/Text] /Length 69 /Length 63 ET 0 g /Type /XObject /FormType 1 endstream 1 i /Matrix [1 0 0 1 0 0] BT /Font << Q 0.737 w endstream (4) Tj /Meta1531 1549 0 R q 1 i Q /Font << >> 0 5.203 TD Q /BBox [0 0 549.552 16.44] >> /Type /XObject stream 0 g /Length 12 /Meta94 108 0 R /FormType 1 /F4 12.131 Tf /Length 78 Q /Widths [ 250 0 0 0 500 0 0 0 333 333 0 0 250 0 << /FormType 1 /BBox [0 0 88.214 35.886] Q /ProcSet[/PDF/Text] >> >> ET /ProcSet[/PDF/Text] endobj endobj /Meta417 431 0 R Q [(3)-25(5\))] TJ BT /FormType 1 /ProcSet[/PDF/Text] /Subtype /Form Q 1633 0 obj >> ET q /Length 152 << Q /BBox [0 0 88.214 35.886] /Resources<< endobj /Length 167 >> /Subtype /Form q /Font << q /FormType 1 0 g /ProcSet[/PDF/Text] /Type /XObject endstream /Matrix [1 0 0 1 0 0] /Length 54 /BBox [0 0 17.177 16.44] /Subtype /Form 2.238 5.203 TD q 0.467 Tc Q /BBox [0 0 639.552 16.44] q /Meta394 Do endstream 0 G /BBox [0 0 534.67 16.44] /Length 78 /F3 12.131 Tf /Meta540 Do /FormType 1 /Resources<< 0 g >> ET /Meta266 Do /Type /XObject >> 0.564 G /Matrix [1 0 0 1 0 0] BT /F4 12.131 Tf q Q /Meta1082 1100 0 R >> /FormType 1 /Type /XObject /Meta30 Do Q Q /Subtype /Form 1.007 0 0 1.007 130.989 289.832 cm /Font << /Font << 0.564 G 1 g ET 0 G endobj q /Subtype /Form 0 5.203 TD 0.564 G endstream /BBox [0 0 15.59 16.44] 0.369 Tc stream (-) Tj /Matrix [1 0 0 1 0 0] stream /Resources<< /Resources<< >> ET q endobj /F3 12.131 Tf Q /Length 78 endobj stream 0.737 w stream q /F3 17 0 R 0.737 w 0 g /ProcSet[/PDF] 1.014 0 0 1.007 251.439 130.236 cm ET /F3 17 0 R 722.699 523.204 l 1.014 0 0 1.006 391.462 807.767 cm q endstream 1.007 0 0 1.007 411.035 236.383 cm /Matrix [1 0 0 1 0 0] q Q q stream /BBox [0 0 534.67 16.44] /F4 12.131 Tf stream /Type /XObject << 98.106 5.336 TD /Matrix [1 0 0 1 0 0] endstream /Length 16 /Length 58 stream BT /FormType 1 /F3 17 0 R >> ET /Matrix [1 0 0 1 0 0] q stream 1 i /F3 17 0 R Q 681 0 obj q Q /ProcSet[/PDF/Text] /Matrix [1 0 0 1 0 0] q << Q stream BT 1402 0 obj 1.005 0 0 1.007 102.382 383.934 cm endstream /Meta757 Do /F3 17 0 R /FormType 1 >> 326 0 obj 377 0 obj /ProcSet[/PDF] 0 g 0.458 0 0 RG endobj 1 i Q /FormType 1 q >> q endstream /Type /XObject /Length 12 /Length 69 /F4 24 0 R endobj /Type /XObject endobj endstream /Font << /FormType 1 1.005 0 0 1.007 102.382 595.474 cm /ProcSet[/PDF/Text] /Font << [(2)-25(3\))] TJ >> /ProcSet[/PDF/Text] /Leading 253 BT /Meta963 Do 1.005 0 0 1.007 102.382 667.744 cm q /FormType 1 1 i /BBox [0 0 673.937 27.581] /F4 12.131 Tf Q q q >> 30.699 5.203 TD BT >> /Resources<< /Length 59 << 0.737 w /Meta577 Do Q >> /Font << stream >> /F4 12.131 Tf S q /Matrix [1 0 0 1 0 0] 1 0 obj (7\)) Tj endobj stream /ProcSet[/PDF] /Resources<< /Length 69 /FormType 1 /FormType 1 >> /Length 69 >> Q Q q -0.092 Tw /Meta231 245 0 R /Resources<< endobj Q 0 w 1.007 0 0 1.007 654.946 735.497 cm /Length 69 1 i /Meta119 Do /BBox [0 0 534.67 16.44] >> Q /BBox [0 0 534.67 16.44] /FormType 1 1 g 1.005 0 0 1.007 102.382 420.822 cm << 1.502 5.203 TD 1.007 0 0 1.007 271.012 183.686 cm /Font << /BBox [0 0 88.214 16.44] /Type /XObject /Length 59 q endstream 0.564 G 0.564 G q endstream stream 1.014 0 0 1.007 391.462 182.933 cm /I0 Do 0.458 0 0 RG /FormType 1 (B) Tj Q stream /Meta326 Do /Length 59 898 0 obj /Subtype /Form 205 0 obj q 1.007 0 0 1.007 67.753 523.204 cm /Length 167 /Type /XObject /FormType 1 /Length 60 >> Q /Resources<< /BBox [0 0 534.67 16.44] >> ET 0 G q << Q /Subtype /Form /Font << 1644 0 obj 1.007 0 0 1.007 271.012 289.832 cm endstream q Q 1 g /Matrix [1 0 0 1 0 0] /Subtype /Form /Length 59 /Type /XObject q >> /FormType 1 stream (5\)) Tj >> /Matrix [1 0 0 1 0 0] Q 0.737 w (C\)) Tj /Subtype /Form Q /ProcSet[/PDF] /Length 69 /Meta325 Do 1 i Q 193 0 obj >> (-) Tj 71 0 obj Q Q q >> >> Level up on all the skills in this unit and collect up to 1500 Mastery points! 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/Type /XObject /Font << q Q << >> /Type /XObject /F4 12.131 Tf /Matrix [1 0 0 1 0 0] << << q /FormType 1 q endobj /Resources<< 0 g /Type /XObject stream ET /ProcSet[/PDF] /Length 12 Q endstream /BBox [0 0 534.67 16.44] /FormType 1 /Length 57 /Matrix [1 0 0 1 0 0] q 0.737 w /F3 17 0 R stream 271 0 obj q /Meta1241 Do /Font << q BT endstream /Type /XObject stream 1.014 0 0 1.006 111.416 307.147 cm /F3 17 0 R Q /Meta1129 1147 0 R /Subtype /Form /Meta355 Do /Matrix [1 0 0 1 0 0] /Matrix [1 0 0 1 0 0] /ProcSet[/PDF] 0 G Q /F3 17 0 R endobj endstream Q 15.731 5.336 TD << endobj /ProcSet[/PDF/Text] /Meta748 764 0 R /F3 12.131 Tf Q /Font << >> /Resources<< Q >> 0 g 1) EMBED Equation.3 2) EMBED Equation.3 3) EMBED Equation.3 4) EMBED Equation.3 5) EMBED Equation.3 6) EMBED Equation.3 REVIEW OF SIMPLIFYING EXPRESSIONS COMPLETE THIS SECTION AFTER QUIZ IS COMPLETED 1) 3a + 7b + 5a 4b 2) 9(2x 8) 3) 15 4 (6n + 3) 4) 6( 3 8b) 5) 12x 5 7x 2 6) 7(8 + 4z) 15z HOW TO SOLVE MULTI-STEP EQUATIONS 1) SIMPLIFY ALL EXPRESSIONS (Distribute, Combine Like Terms, Evaluate) 2) IDENTIFY VARIABLE 3) CANCEL Operations using their opposites in reverse order of operations EXAMPLES: 1) 7x + 5 3x = 17 2) 9(x + 4) = 63 3) 4(2y 3) = 28 4) 7(6 x) = 56 5) 3(8+ n) 15 = 24 6) EMBED Equation.3 7) 19 = 9 + 2(x 7) 8) EMBED Equation.3 9) 4(3y 5) 7y = - 60 CC MATH I STANDARDS UNIT 3 4.5 SOLVING MULTI-STEP EQUATIONS: PART 2 WARM UP: Simplify each of the following expressions 1) EMBED Equation.3 2) EMBED Equation.3 3) EMBED Equation.3 4) EMBED Equation.3 5) EMBED Equation.3 6) EMBED Equation.3 SOLVE THE FOLLOWING ONE and TWO STEP EQUATIONS 1) EMBED Equation.3 2) EMBED Equation.3 3) EMBED Equation.3 4) EMBED Equation.3 5) EMBED Equation.3 6) EMBED Equation.3 7) EMBED Equation.3 8) EMBED Equation.3 PRACTICE: SOLVE MULTISTEP EQUATIONS 1) 10x 7x = 12 2) 9z + 11 5z = 27 3) 7 + 6n 9 = - 4 4) 6(y + 7) = 66 5) -3(4x + 9) = 15 6) 5(1 2x) = - 65 7) 8 + 3(r + 5) = 5 8) 15 2 ( 7 x) = 7 9) 7(3 + 4y) 15y = 73 10) EMBED Equation.3 11) EMBED Equation.3 12) EMBED Equation.3 CC MATH I STANDARDS UNIT 3 4.5 SOLVING MULTI-STEP EQUATIONS: PART 3 WARM UP PART 1: Simplify each expression 1) EMBED Equation.3 2) EMBED Equation.3 3) EMBED Equation.3 WARM UP PART 2: Solve each equation 4) EMBED Equation.3 5) EMBED Equation.3 6) EMBED Equation.3 7) EMBED Equation.3 8) EMBED Equation.3 9) EMBED Equation.3 10) EMBED Equation.3 HOMEWORK: SOLVE EACH EQUATION #1 14 10/22 Use a separate piece of paper as needed Reduce all fraction answers EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 MATCH SOLUTIONS BELOW WITH THE EQUATIONS ABOVE 2 4 -3 -5 -1/2 1 1/3 -2 3 -7 9 11 3/2 BONUS: ADVANCED PROBLEMS B#1) 3(2x + 4) 2(5 x) = 66 B#2) EMBED Equation.3 ' ( - = E F M l m n o r s zkbYM>4 h h[= 5CJ j h h[= 5CJ U h[= h[= 56CJ h`J+ 56CJ h[ h[= CJ h[ h[= 56CJ \] h[ h$w 56CJ \] h[ h[= 56>*CJ \]h[ hV} 56CJ \] h[ h 56CJ \] h[ h 56>*CJ \]h[ h$w 56>*CJ \]h[ hV} 56>*CJ \]h[ hy6 56>*CJ \]h[ hV} CJ F m n o gd$w gd[= $ a$ gd[= $a$ wf]I8] j h[= h$w 5CJ EHU &j2)T stream 0 G 0 G 1 i q /Meta858 Do 1.007 0 0 1.007 411.035 290.585 cm /ProcSet[/PDF/Text] /Matrix [1 0 0 1 0 0] q endstream endobj /FormType 1 >> stream /Type /XObject >> Q 1.007 0 0 1.007 67.753 367.372 cm q 0 g Q /Meta1588 1608 0 R 0.567 Tc Q Q /Subtype /Form endobj /Meta1525 Do endobj stream /F3 17 0 R Q q BT /F3 12.131 Tf 0 21.617 TD Q /Length 69 /BBox [0 0 88.214 16.44] q 0.737 w 1 i Q /Meta1042 1058 0 R >> /BBox [0 0 534.67 16.44] Q 722 0 obj >> /Resources<< /Resources<< /Subtype /Form endstream Q 0 g /Resources<< /Type /XObject /Matrix [1 0 0 1 0 0] Q q << /Meta16 Do 0.388 Tc q /Meta157 171 0 R /Resources<< endstream 0 G /Subtype /Form /Font << q q << >> /FormType 1 /Meta830 Do 15.731 5.336 TD 0.524 Tc 0 w endobj 1 i BT q /ProcSet[/PDF/Text] Q /BBox [0 0 88.214 35.886] /BBox [0 0 30.642 16.44] 1 g 0.297 Tc ET >> 0.68 Tc /Resources<< /Subtype /Form Q /FormType 1 >> << /Type /XObject >> 1 i /BBox [0 0 15.59 16.44] /Length 16 722.699 576.654 l /Resources<< /FormType 1 BT /Subtype /Form endstream << /FormType 1 /Length 59 q q q /F3 17 0 R /ProcSet[/PDF/Text] << 0 g /Resources<< Q q 1.005 0 0 1.007 79.798 283.057 cm /F4 24 0 R 1 i stream /Length 59 << /Meta143 157 0 R /Font << 0.524 Tc /Subtype /Form Q q /XObject << endobj /F3 12.131 Tf Q 1.005 0 0 1.007 102.382 416.305 cm /Meta71 85 0 R 775 0 obj 1.502 24.649 TD Q /F3 12.131 Tf Q endobj 0.838 Tc Q >> /FormType 1 /Matrix [1 0 0 1 0 0] /Length 59 1.502 5.203 TD /Meta1446 1464 0 R endobj /FormType 1 696 0 obj /ProcSet[/PDF/Text] 0 g /Type /XObject /Subtype /Form 0 g /Matrix [1 0 0 1 0 0] /Meta1487 Do /ProcSet[/PDF/Text] q >> /Length 16 /Meta1455 Do /ProcSet[/PDF/Text] /Matrix [1 0 0 1 0 0] /Length 78 /F4 12.131 Tf /BBox [0 0 534.67 35.886] /ProcSet[/PDF] Q q >> endobj /Subtype /Form /Type /XObject q endstream >> /Meta116 Do /Parent 1 0 R /Resources<< 1 i 0 g 1 i /Subtype /Form /Resources<< /Subtype /Form 0 g endobj << /Font << 1 i Q ET /Resources<< /F3 17 0 R 29.196 17.903 TD >> 1.005 0 0 1.007 79.798 713.666 cm

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