Questions: Solve for (h). [ -3(2 h+1) leq-4 h+7 ] (h leq-5) (h geq-2) (h geq-5) (h leq 1 frac12)

$Solve for (h). [ -3(2 h+1) leq-4 h+7 ] (h leq-5) (h geq-2) (h geq-5) (h leq 1 frac12)$

Transcript text: Solve for $h$. \[ -3(2 h+1) \leq-4 h+7 \] $h \leq-5$ $h \geq-2$ $h \geq-5$ $h \leq 1 \frac{1}{2}$

Solution

Step 1: Distribute the -3

Distribute the $-3$ across the terms inside the parentheses: \[ -3(2h + 1) \leq -4h + 7 \implies -6h - 3 \leq -4h + 7 \]

Step 2: Move all terms involving $ h $ to one side

Add $6h$ to both sides to get all terms involving $ h $ on one side: \[ -6h - 3 + 6h \leq -4h + 7 + 6h \implies -3 \leq 2h + 7 \]

Step 3: Isolate the term with $ h $

Subtract 7 from both sides to isolate the term with $ h $: \[ -3 - 7 \leq 2h \implies -10 \leq 2h \]

Step 4: Solve for $ h $

Divide both sides by 2 to solve for $ h $: \[ \frac{-10}{2} \leq h \implies -5 \leq h \]

$\boxed{h \geq -5}$

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