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What is the solution set of this inequality? [tex]\[ 8(x-5) - 3x \geq -20 \][/tex]
A. [tex]\( x \geq 4 \)[/tex] B. [tex]\( x \leq 12 \)[/tex] C. [tex]\( x \leq -12 \)[/tex] D. [tex]\( x \geq -3 \)[/tex]
To solve the inequality [tex]\( 8(x-5) - 3x \geq -20 \)[/tex], follow these steps:
1. Distribute the 8 across the term [tex]\((x-5)\)[/tex]: [tex]\[
8(x-5) - 3x \geq -20
\][/tex] becomes: [tex]\[
8x - 40 - 3x \geq -20
\][/tex]
2. Combine like terms on the left-hand side: [tex]\[
(8x - 3x) - 40 \geq -20
\][/tex] simplifies to: [tex]\[
5x - 40 \geq -20
\][/tex]
3. Add 40 to both sides of the inequality to isolate the term with [tex]\(x\)[/tex]: [tex]\[
5x - 40 + 40 \geq -20 + 40
\][/tex] simplifies to: [tex]\[
5x \geq 20
\][/tex]
4. Divide both sides by 5 to solve for [tex]\(x\)[/tex]: [tex]\[
\frac{5x}{5} \geq \frac{20}{5}
\][/tex] simplifies to: [tex]\[
x \geq 4
\][/tex]
Thus, the solution set of the inequality [tex]\( 8(x-5) - 3x \geq -20 \)[/tex] is: [tex]\[
x \geq 4
\][/tex]
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