Question

solve the inequality -3(4x + 3) + 2(12x + 3) < -53.

question 3
2 points
solve the inequality -5 + 25x + 10(-4x - 1) > -4x - 8x: (fill each blank with an integer or inequality symbol)

Explanation:

Step1: Expand left-hand side

$-3(4x+3)+2(12x+3) = -12x -9 +24x +6$

Step2: Simplify the expression

$-12x -9 +24x +6 = 12x -3$

Step3: Isolate the variable term

$12x -3 < -63 \implies 12x < -63 + 3$

Step4: Solve for x

$12x < -60 \implies x < \frac{-60}{12} \implies x < -5$
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Step1: Expand left-hand side

$-5 +25x +10(-4x-1) = -5 +25x -40x -10$

Step2: Simplify the expression

$-5 +25x -40x -10 = -15x -15$

Step3: Rearrange terms to isolate x

$-15x -15 > -4x -8 \implies -15 +8 > -4x +15x$

Step4: Solve for x

$-7 > 11x \implies x > \frac{-7}{-7} \implies x > 1$

Answer:

1. $x < -6$
2. $x > 1$