Question

1. which expression is equivalent to (2 + 3(x - 5)+4)?

a. (3x + 9)
b. (3x - 9)
c. (3x + 1)
d. (x - 9)

1. what is the solution to the equation (-5x - 6x + 9x = 2.4)?

a. (-1.2)
b. (1.2)
c. (4.8)
d. (-4.8)

1. for each expression, write an equivalent expression with fewer terms. show your thinking.

a (3(x + 4)-9)
b (\frac{1}{4}(4x + 12)-(3x + 2))
c (6 - 2(x + 8)-4)

1. solve each equation. show your thinking.

a (10b - 5b - 7b = 4.4)
b (-4(-c - 2)-6c = 3.8)
c (-\frac{2}{3}(3x - 9)-2x = 8)
d (\frac{1}{4}(6w - 12)+0.5w = 16)

Explanation:

Step1: Expand the parentheses

$2 + 3x - 15 + 4$

Step2: Combine like terms

$3x + (2 - 15 + 4) = 3x - 9$

Step1: Combine like terms

$(-5 - 6 + 9)x = 2.4$
$-2x = 2.4$

Step2: Solve for $x$

$x = \frac{2.4}{-2} = -1.2$

Part a

Step1: Expand the parentheses

$3x + 12 - 9$

Step2: Combine constants

$3x + (12 - 9) = 3x + 3$

Part b

Step1: Simplify the fraction term

$\frac{1}{4}(4x) + \frac{1}{4}(12) - 3x - 2 = x + 3 - 3x - 2$

Step2: Combine like terms

$(x - 3x) + (3 - 2) = -2x + 1$

Part c

Step1: Expand the parentheses

$6 - 2x - 16 - 4$

Step2: Combine constants

$-2x + (6 - 16 - 4) = -2x - 14$

Part a

Step1: Combine like terms

$10 - 12b = 4.4$

Step2: Isolate the variable term

$-12b = 4.4 - 10 = -5.6$

Step3: Solve for $b$

$b = \frac{-5.6}{-12} = \frac{7}{15} \approx 0.47$

Part b

Step1: Expand the parentheses

$4c + 8 - 6c = 3.8$

Step2: Combine like terms

$-2c + 8 = 3.8$

Step3: Isolate the variable term

$-2c = 3.8 - 8 = -4.2$

Step4: Solve for $c$

$c = \frac{-4.2}{-2} = 2.1$

Part c

Step1: Expand the parentheses

$-\frac{2}{3}(3x) + \frac{2}{3}(9) - 2x = 8$
$-2x + 6 - 2x = 8$

Step2: Combine like terms

$-4x + 6 = 8$

Step3: Isolate the variable term

$-4x = 8 - 6 = 2$

Step4: Solve for $x$

$x = \frac{2}{-4} = -0.5$

Part d

Step1: Expand the parentheses

$\frac{3}{4}(6w) - \frac{3}{4}(12) + 0.5w = 16$
$4.5w - 9 + 0.5w = 16$

Step2: Combine like terms

$5w - 9 = 16$

Step3: Isolate the variable term

$5w = 16 + 9 = 25$

Step4: Solve for $w$

$w = \frac{25}{5} = 5$

Answer:

B. $3x - 9$

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