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

$x + 1 \leq 3$

Steps

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

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

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

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 ： $x + 1 \leq 3$