Question

simplify the following expressions by using distributive property and combining like terms.
#6) 10x + 2(3x − 1) #7) 7 − 2(x − 3)
#8) 5x + 2x + 4(2x − 3)
solve the following equations.
#9) -3x + 1 = 19 #10) -3(2x − 4) + 10 = 5 #11) -2x + 5 = 9x − 1

Explanation:

#6 Step1: Apply distributive property

$10x + 2(3x) - 2(1) = 10x + 6x - 2$

#6 Step2: Combine like terms

$10x + 6x - 2 = 16x - 2$

#7 Step1: Apply distributive property

$7 - 2(x) + 2(3) = 7 - 2x + 6$

#7 Step2: Combine constant terms

$7 + 6 - 2x = 13 - 2x$

#8 Step1: Combine initial like terms

$5x + 2x + 4(2x - 3) = 7x + 4(2x - 3)$

#8 Step2: Apply distributive property

$7x + 4(2x) - 4(3) = 7x + 8x - 12$

#8 Step3: Combine like terms

$7x + 8x - 12 = 15x - 12$

#9 Step1: Isolate the x-term

$-3x = 19 - 1$
$-3x = 18$

#9 Step2: Solve for x

$x = \frac{18}{-3}$
$x = -6$

#10 Step1: Apply distributive property

$-3(2x) + 3(4) + 10 = 5$
$-6x + 12 + 10 = 5$

#10 Step2: Combine constants

$-6x + 22 = 5$

#10 Step3: Isolate the x-term

$-6x = 5 - 22$
$-6x = -17$

#10 Step4: Solve for x

$x = \frac{-17}{-6} = \frac{17}{6}$

#11 Step1: Group x-terms on one side

$-2x - 9x = -1 - 5$

#11 Step2: Simplify both sides

$-11x = -6$

#11 Step3: Solve for x

$x = \frac{-6}{-11} = \frac{6}{11}$

Answer:

#6) $16x - 2$
#7) $13 - 2x$
#8) $15x - 12$
#9) $x = -6$
#10) $x = \frac{17}{6}$
#11) $x = \frac{6}{11}$