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Math  /  Algebra

Question5) −50≥2q+3q-50 \geq 2 q+3 q 10) 2(4−3g)−5g<6g−1282(4-3 g)-5 g<6 g-128

Studdy Solution

STEP 1

1. We are solving two separate inequalities.
2. For each inequality, we will isolate the variable on one side to find the solution.
3. We will simplify expressions and solve linear inequalities.

STEP 2

1. Solve the inequality −50≥2q+3q -50 \geq 2q + 3q .
2. Solve the inequality 2(4−3g)−5g<6g−128 2(4 - 3g) - 5g < 6g - 128 .

STEP 3

Simplify the expression on the right side of the inequality −50≥2q+3q -50 \geq 2q + 3q :
Combine like terms: 2q+3q=5q 2q + 3q = 5q
The inequality becomes: −50≥5q -50 \geq 5q

STEP 4

Solve for q q by dividing both sides by 5:
−505≥q \frac{-50}{5} \geq q
−10≥q -10 \geq q
This can also be written as: q≤−10 q \leq -10

STEP 5

Expand the expression on the left side of the inequality 2(4−3g)−5g<6g−128 2(4 - 3g) - 5g < 6g - 128 :
Distribute the 2: 2×4−2×3g=8−6g 2 \times 4 - 2 \times 3g = 8 - 6g
The inequality becomes: 8−6g−5g<6g−128 8 - 6g - 5g < 6g - 128
Combine like terms: 8−11g<6g−128 8 - 11g < 6g - 128

STEP 6

Isolate the variable g g by first adding 11g 11g to both sides:
8<17g−128 8 < 17g - 128
Next, add 128 to both sides to further isolate terms involving g g :
8+128<17g 8 + 128 < 17g
136<17g 136 < 17g

STEP 7

Solve for g g by dividing both sides by 17:
13617<g \frac{136}{17} < g
8<g 8 < g
This can also be written as: g>8 g > 8
The solutions to the inequalities are:
1. q≤−10 q \leq -10
2. g>8 g > 8

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