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Answer
The solution to the inequality is \( x \geq -\frac{6}{5} \).
Solution
We start with the inequality:
3 - 5(2x + 1) ≤ 10
Step 1: Distribute -5 inside the parentheses:
3 - 10x - 5 ≤ 10
Step 2: Combine like terms:
-10x - 2 ≤ 10
Step 3: Add 2 to both sides to isolate the term with x:
-10x ≤ 12
Step 4: Divide both sides by -10. Remember that dividing by a negative number reverses the inequality sign:
x ≥ -12/10
Step 5: Simplify the fraction:
x ≥ -6/5
Thus, the solution to the inequality is:
x ≥ -6/5
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Simplify this solution The Deep Dive
To solve the inequality \( 3-5(2 x+1) \leq 10 \), let's start by distributing the \(-5\): \[ 3 - 10x - 5 \leq 10 \] Next, simplify the left side: \[ -10x - 2 \leq 10 \] Now, add \(2\) to both sides: \[ -10x \leq 12 \] Then, divide both sides by \(-10\). Remember, when you divide by a negative number, you need to flip the inequality sign: \[ x \geq -\frac{12}{10} \] Simplifying that gives: \[ x \geq -\frac{6}{5} \] So the solution to the inequality is: \[ x \geq -\frac{6}{5} \] This means any number greater than or equal to \(-1.2\) will satisfy the inequality.
