8x – 3x + 2x + 15 – 7x Distributive Property Classwork Use the Distributive Property to rewrite the expressions without parentheses (x + 4) 8(x – 2) 6(x + 4) -1(x – 4) (x + 2)8 ⅝(4x + 12) 1.2(3x – 7.1) Use the Distributive Property to factor the following expressions 5x + 35 2x + 24x 7r + 42t 3j + 24k + 33m 4x2 + 20x -9p + 6q -15n – 45v If a square has a perimeter of 8x + 36, how much is each side? Homework Use the Distributive Property to rewrite the expressions without parentheses 5(x + 4) 7(x – 12) 3(x - 14) -1(x – 2) (x - 2)5 ⅔(6x + 12) 2.5(3x – 4.1) Use the Distributive Property to factor the following expressions 12b + 48 6m + 14m 16y + 56z 8e + 24f + 28g 12d2 + 15d -14r + 21t -9c – 15h If a triangle has a perimeter of 12w + 18, how much is each side? Simplifying Algebraic Expressions Classwork Simplify the algebraic expression if possible.
-8 + r = 27 19 + m = 3 p – 4.8 = 11.2 3.6m = 25.2 Two Step Equations Classwork Solve. 7x – 2 = 26 ½ (m – 3) = 12 -6h – 6 = 30 5x + 20 = -20 3 = -3y – 15 -24 = 14y – 5 7r – 5 = 10 9 = 16y + 51 13x + 6 = 6 -4.5x + 12.3 = -23.7 5.4x – 8.3 = 14.38 Homework 2m – 8 = -28 12m + 20 = -40 8r – 27 = -19 15 = -4y – 9 8w + 4 = -36 4a – 15 = -23 44 = 5x – 6
x+4 8x-16 6x+24 –x+4 8x+16 3.6x - 8.52 8. 5(x+7) 2(x+12) 7(r+6t) 3(j+8k+11m) 4x(x+5) 3(-3p+2q) -15(n+3v) 2x + 9 10. 5x + 20 7x – 84 3x – 42 –x + 2 5x – 10 4x +8 7.5x – 10.25 11. 12(b + 4) 2m (3 + 7) 8(2y + 7z) 4(2e + 6f + 7g) 3d(4d + 5) 7(-2r + 3t) -3(3c + 5h) 4w + 6 a. 10x + 10y +9 b. 4x + 7y c. 4x + 7 d. 7x + 12 e. 7x + 15 f. 35x + 3 g. 10x + 10y h. 2x + 6 i. 7x + 16 j. 16x + 24 k. 2x l. 7x + 19 m. 16x – 24 n. 3x + 45 14. a. 9x + 10y + 12 b. 8x + 3y c. 25x -15 d. 53x + 13 e. -9 f. 51x + 11 g. 21x + 11y h. 7x + 2 i. 11x + 35 j. 52v + 46 k. -8k + 44 l. 12j + 3x + 37 m. 26x + 34 n. -3t + 29 Subtraction Addition Subtraction Multiplication Division Addition Division Subtraction Division Multiplication 13 -17 42 6 42 22 128 2 ½ -5 72 8 6 62 -10 10.5 4.5 9 4 35 4 -5 4 17 99 20 15 75 5 35 -16
-8 16 7.48 7 4 27 -6 -8 -6 -19/14 15/7 -21/8 0 24 8 0.5 -15.3 4.2 -10 99 -5 -48 1 81 -6 -5 -2 10 3.1 3.3 -16.8 5 18.66 or 14 0.166 11 14 3 1 2 ½ -9 1 2.5 3 6.1 5.2 -8 3 3 -3/7 13 10 24 0.86 11 4.7 -5 8.4 6 11 14 1 ½ -6 -4 ½ 2 3 23 3 5 -4/5 -2 7 2 -2 a. 4 + 3x + x = 112; x = 85 4w + 10 = 90; 20 4(x – 3) = x – 27; -5 3(21 + n) = 12; -17 a. 6b + 36 = 84; 8 and 20 b. 4L – 26 = 90; 29 c. 6(n-9) = n – 19; 35 d. 56 + 8n = 16; -5 Selina $76 $51.36 31 red, 93 blue 7 games Jerrell $45 $927.72 brother = 9, Lorena = 18 3 sodas y < 8 f > -5 j ≥ 4 s < 55
10 < x x ≥ 15 h < 4 x < 20 z < 0 g > 70 k < -3 t < 8 -2 < n t < 20 4 ≥ s x>-2 x<7 x≥2 x<6 x<5 x≥-75 w>7 p<-1 m<5 11≥k f>0 t<4 4<n s<25 x≥12 w<50 g≥8 h≥-5 t<30 25≥s g>92 x≥-6 x<-2 x<4 x>0 x>-10 x≥2.5
Opened: if possibility of being not equal to, Closed: if possibility of equal to x>5 x<-5 -4≥x x<-2 x>10 x≥0 -6<x x<3.5 -2.5<x 6.5>x w+9<18, w<9 g-25<5, g<30 x-6≥15, x≥21 14>10+x, 4>x 25+x≥13, x≥-12 542-57+x≥500, x≥15 650+825+c<2200, c<725 x>-9 x<-6 -23<x x<5 x>7 x≥-4 -4<x x<3.5 -2.25<x 3.5>x x-7<16, x<23 18<x+7, 11<x h-3>1, h>4 14≥18+x, -4≥x b+22≥6, b≥-16 612+79-x≥500, 191≥x 720+1000+c<2200, c<480 x>-5 x≥3 9>x x≥4 5≥x x<0 x≥3 5≥x x≥3/2
5<x x≥10 x<28 18≥x x<-9 x<12 x<9 0<x -2.5≥x x>-2.2 x<15 5r<55, r<11 v/(-4) ≥2, v<-8 (d/2)>40, d>80 2x<24, x<12 (y/4) <-12, <48 -8x≥-64, x<8 Nothing Nothing Nothing Nothing Change to the opp. inequality sign Change to the opp. inequality sign x<-4 4<x x<-7 x>11 x≥0 5<x -22<x x<-60 x<8.5 6.5<x 15<x x<-9 x<0 x>33 -4≥x 24<x x<6