Question

question 4
complete the inequality after solving 2(3x + 14) + 640x > 16(x - 4) + 28. (fill each blank with a number or inequality symbol.)
x ____ ____
question 5
complete the inequality after solving -(4x + 2) + 10 > \frac{1}{3}(x + 6) - 4x + 9. (fill each blank with an integer or inequality symbol.)
x ____ ____

Explanation:

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Question 4

Step1: Expand all parentheses

$2(8x+14)+640x > 16(x-4)+28$
$16x + 28 + 640x > 16x - 64 + 28$

Step2: Combine like terms

$656x + 28 > 16x - 36$

Step3: Isolate x terms

$656x - 16x > -36 - 28$
$640x > -64$

Step4: Solve for x

$x > \frac{-64}{640}$
$x > -1$

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Question 5

Step1: Expand all parentheses

$-(4x+2)+10 > \frac{1}{2}(x+6)-4x+9$
$-4x - 2 + 10 > \frac{1}{2}x + 3 - 4x + 9$

Step2: Combine like terms

$-4x + 8 > -\frac{7}{2}x + 12$

Step3: Isolate x terms

$-4x + \frac{7}{2}x > 12 - 8$
$-\frac{1}{2}x > 4$

Step4: Solve for x (reverse inequality)

$x < 4 \times (-2)$
$x < 1$

Answer:

Question 4: $x > -1$
Question 5: $x < 1$