Question

solve $10x + 16 geq 6x + 20$.

a. $x geq 9$

b. $x leq 9$

c. $x geq 1$

d. $x leq 1$

Explanation:

Step1: Subtract \(6x\) from both sides

To isolate the \(x\) terms, we subtract \(6x\) from both sides of the inequality \(10x + 16 \geq 6x + 20\). This gives us \(10x - 6x + 16 \geq 6x - 6x + 20\), which simplifies to \(4x + 16 \geq 20\).

Step2: Subtract 16 from both sides

Next, we subtract 16 from both sides to further isolate the term with \(x\). So, \(4x + 16 - 16 \geq 20 - 16\), which simplifies to \(4x \geq 4\).

Step3: Divide both sides by 4

Finally, we divide both sides of the inequality \(4x \geq 4\) by 4. This gives us \(\frac{4x}{4} \geq \frac{4}{4}\), which simplifies to \(x \geq 1\).

Answer:

C. \(x \geq 1\)