D) $x$ can be all real numbers
7. If $x+6 \geq 5 x-2$, which of the following inequalities gives all possible values for $x+1$ ?
A) $x+1 \leq 2$
B) $x+1 \geq 3$
C) $x+1 \leq 3$
D) $x+1 \geq 2$

Answer

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Answer

$\boxed{x+1 \leq 3}$

Steps

Step 1 ：Solve the inequality $x+6 \geq 5x-2$ for $x$

Step 2 ：Subtract $x$ from both sides: $6 \geq 4x-2$

Step 3 ：Add $2$ to both sides: $8 \geq 4x$

Step 4 ：Divide both sides by $4$: $2 \geq x$

Step 5 ：Find the possible values for $x+1$

Step 6 ：Since $x \leq 2$, then $x+1 \leq 3$

Step 7 ：$\boxed{x+1 \leq 3}$