13x+2>3((2x+1)-x+8
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What is the purpose of the double beginning parentheses?
3((2x+1
To simplify and solve the inequality 13x + 2 > 3((2x + 1) - x + 8), we can follow a step-by-step approach:
Step 1: Simplify the expression on the right-hand side using the distributive property.
2x + 1 - x + 8 = 2x - x + 1 + 8 = x + 9
After simplifying, the inequality becomes 13x + 2 > 3(x + 9).
Step 2: Distribute the 3 on the right-hand side.
3(x + 9) = 3x + 27
Now we have 13x + 2 > 3x + 27.
Step 3: To solve the inequality, we want to isolate x on one side of the inequality.
Subtract 3x from both sides to eliminate the variable term from the right side:
13x + 2 - 3x > 3x + 27 - 3x
This simplifies to 10x + 2 > 27.
Step 4: Next, subtract 2 from both sides to isolate the 10x term on the left side:
10x + 2 - 2 > 27 - 2
This simplifies to 10x > 25.
Step 5: Divide both sides of the inequality by 10 to solve for x:
(10x)/10 > 25/10
This simplifies to x > 2.5.
So, the solution to the inequality 13x + 2 > 3((2x + 1) - x + 8) is x > 2.5.