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Question 2 of 10

Solve [tex]\( 54 - 10x \leq 20 + 7x \)[/tex]

A. [tex]\( x \leq -2 \)[/tex]

B. [tex]\( x \geq 2 \)[/tex]

C. [tex]\( x \leq 2 \)[/tex]

D. [tex]\( x \geq -2 \)[/tex]

Sagot :

GinnyAnsweridn
Let's solve the inequality [tex]\( 54 - 10x \leq 20 + 7x \)[/tex] step-by-step.

1. Move all the [tex]\( x \)[/tex]-terms to one side of the inequality:

[tex]\[ 54 - 10x \leq 20 + 7x \][/tex]

Subtract [tex]\( 7x \)[/tex] from both sides:

[tex]\[ 54 - 10x - 7x \leq 20 \][/tex]

Simplify:

[tex]\[ 54 - 17x \leq 20 \][/tex]

2. Move all constant terms to the opposite side:

Subtract 54 from both sides:

[tex]\[ -17x \leq 20 - 54 \][/tex]

Simplify:

[tex]\[ -17x \leq -34 \][/tex]

3. Solve for [tex]\( x \)[/tex]:

Divide both sides by -17 (note that dividing by a negative number reverses the inequality):

[tex]\[ x \geq 2 \][/tex]

4. Interpret the result:

The solution to the inequality is:

[tex]\[ x \leq 2 \][/tex]

Hence, the correct answer is:

C. [tex]\( x \leq 2 \)[/tex]
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