Of course! Let's solve the inequality step-by-step.
Given the inequality:
[tex]\[ 13x - 6 \geq 8x + 54 \][/tex]
1. Eliminate the variable on one side:
To do this, we want to isolate [tex]\(x\)[/tex] on one side of the inequality. We can start by subtracting [tex]\(8x\)[/tex] from both sides:
[tex]\[ 13x - 8x - 6 \geq 8x - 8x + 54 \][/tex]
2. Simplify the inequality:
[tex]\[ 5x - 6 \geq 54 \][/tex]
3. Isolate [tex]\(x\)[/tex] by adding 6 to both sides:
[tex]\[ 5x - 6 + 6 \geq 54 + 6 \][/tex]
[tex]\[ 5x \geq 60 \][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 5:
[tex]\[ \frac{5x}{5} \geq \frac{60}{5} \][/tex]
[tex]\[ x \geq 12 \][/tex]
So, the solution to the inequality [tex]\( 13x - 6 \geq 8x + 54 \)[/tex] is:
[tex]\[ x \geq 12 \][/tex]
Therefore, [tex]\( x \)[/tex] must be at least 12 for the inequality to hold true.
