Math  /  Algebra

QuestionQuestion 2 (6points) 8x+12>10x+188 x+12>10 x+18
Put the steps for solving this in the proper order 8x+1212>10x+18128x10x>10x10x+62x>622x<628x>10x+6\begin{array}{l} 8 x+12-12>10 x+18-12 \\ 8 x-10 x>10 x-10 x+6 \\ -2 x>6 \\ \frac{-2}{-2} x<\frac{6}{-2} \\ 8 x>10 x+6 \end{array}

Studdy Solution

STEP 1

1. The inequality 8x+12>10x+18 8x + 12 > 10x + 18 is asking us to find the values of x x that satisfy the inequality.
2. This is a linear inequality involving basic algebraic operations.
3. The solution will involve isolating the variable x x .

STEP 2

1. Simplify the inequality by eliminating constants from one side.
2. Isolate the variable x x by performing algebraic operations.
3. Solve the inequality and consider the direction of the inequality sign.

STEP 3

Start by eliminating the constant term on the left side of the inequality:
8x+1212>10x+1812 8x + 12 - 12 > 10x + 18 - 12
This simplifies to:
8x>10x+6 8x > 10x + 6

STEP 4

Next, eliminate the 10x 10x term from the right side by subtracting 10x 10x from both sides:
8x10x>10x10x+6 8x - 10x > 10x - 10x + 6
This simplifies to:
2x>6 -2x > 6

STEP 5

Now, solve for x x by dividing both sides by 2-2. Remember that dividing by a negative number reverses the inequality sign:
2x2<62 \frac{-2x}{-2} < \frac{6}{-2}
This simplifies to:
x<3 x < -3
The solution to the inequality is:
x<3 x < -3

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