How to find the solution to an inequality with addition

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Algebra › How to find the solution to an inequality with addition

Questions 1 - 10

Solve:

$\small x+2\geq 7$

$\small x\geq 5$

$\small x\leq 9$

$\small x> 5$

$\small x< 9$

None of the other answers are correct.

Explanation

Subtract 2 from each side:

$\small x+2-2\geq 7-2$

$\small x\geq 5$

Solve for :

Explanation

Subtracting and adding 3 to both sides of the equation of will give you . Divide both sides by 2 to get .

Solve for :

None of the other answers

Explanation

To solve the inequality, simply move the 's to one side and the integers to the other (i.e. subtract from both sides and add 9 to both sides). This gives you .

Solve for :

Explanation

This inequality can be solved just like an equation.

Add 4 to both sides:

2x > 11

Then divide by 2:

x > 11/2 = 5.5

Solve the inequality: $x-9\leq 8$

$x\leq 17$

$x\geq 17$

$x\leq -1$

Explanation

To solve this inequality, simply add nine on both sides.

$x-9+9\leq 8+9$

Simplify both sides of the inequality.

$x\leq 17$

The answer is: $x\leq 17$

Solve the inequality: $z-3\geq 16$

$z\geq 19$

$z\leq 19$

$z\leq13$

$z\geq13$

Explanation

In order to solve this inequality, add three on both sides.

$z-3+3\geq 16+3$

Simplify both sides of the inequality.

The answer is: $z\geq 19$

Solve the inequality:

$x\leq 35$

$x\geq35$

Explanation

In order to solve for the unknown variable, add 12 on both sides.

Simplify both sides.

The answer is:

Solve the following inequality:

Explanation

Add both sides by four to isolate the variable.

Simplify both sides of the equation.

The answer is:

This means that is greater than forty, but cannot equal to forty.

Solve this inequality:

$12x-5\geq-4x+43$

$x\geq3$

$x\geq4$

Not enough information to be determined.

$x\geq6$

$x\geq2$

Explanation

To solve this inequality, we need to separate the constants from the variables so that they are on opposite sides of the inequality.

We can do this by adding (4x+5) to each side and

$12x-5+(4x+5)\geq-4x+43 + (4x+5)$ .

The constants cancel on the left side, and the variables cancel on the right side.

$16x+0\geq0x+48$

$16x\geq48$

Then, we divide both sides by 16, to get our final answer:

$\frac{16x}{16}\geq\frac{48}{16}$

$x\geq 3$

Solve the inequality:

$\small 15x - 4 \le 2x + 8 +x$

$\small x \le1$

$\small x \le \frac{6}{7}$

$\small x \le \frac{4}{5}$

$\small x \le 0$

$\small x \le \frac{11}{14}$

Explanation

First, combine like terms on a single side of the inequality. On the right side of the inequality, combine the terms to obtain $\small 15x - 4 \le 3x +8$ .

Next, we want to get all the variables on the left side of the inequality and all of the constants on the right side of the inequality. Add 4 to both sides and subtract from both sides to get $\small 12x \le 12$ .

Finally, to isolate the variable, divide both sides by 12 to produce the final answer, $\small x \le1$ .

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