3(7+2x)¡Ü 30+7 (x-1)
The answer to this inequality problem is x ¡Ý -2
I can't figure out how they got this answer. Can you show me the steps?
Sure! I can help explain the steps to solve this inequality problem.
Step 1: Start by simplifying both sides of the inequality.
On the left side, apply the distributive property by multiplying the 3 with each term inside the parentheses:
3 * 7 = 21
3 * 2x = 6x
So the left side becomes: 21 + 6x.
On the right side, simplify the expression inside the parentheses:
7 * (x - 1) = 7x - 7.
So the right side becomes: 30 + 7x - 7.
Step 2: Rewrite the inequality with the simplified expressions.
The inequality becomes:
21 + 6x ≤ 30 + 7x -7.
Step 3: Rearrange the equation to group like terms on one side.
To do this, move the 7x term to the left side by subtracting 7x from both sides:
21 - 7x + 6x ≤ 30 - 7.
Simplifying further:
21 - x ≤ 23.
Step 4: Solve for x by isolating the variable on one side.
To isolate x, subtract 21 from both sides:
21 - x - 21 ≤ 23 - 21.
Simplifying:
-x ≤ 2.
Step 5: Divide both sides of the inequality by -1.
When multiplying or dividing an inequality by a negative number, remember to reverse the inequality sign. In this case, divide both sides of the inequality by -1, which reverses the sign:
(-x)/(-1) ≥ (2)/(-1).
Simplifying:
x ≥ -2.
Thus, the solution to the inequality is x ≥ -2.
So, the answer to the inequality problem x ≥ -2 is correct.