Solve a linear inequality with simple operations - High school Algebra I Exercises

Solve the following linear inequalities using simple operations.

6-3x ≤ -12

x≤-6

x ≥ 6

x≥-6

x≤6

Solve the equation:

6-3x ≤ -12

Move the constant term, 6, to the right side by subtracting 6 from both sides of the inequality:

6-3x-6 ≤ -12-6

-3x \leq -18

Divide both sides of the inequality by -3, and switch the direction of the inequality as -3 is negative:

\dfrac{-3x}{-3} \geq \dfrac{-18}{-3}

x \geq 6

The set of solutions is \left[ 6,+\infty \right).

5-3x ≤ -10

x\leq 5

x \geq -5

x\leq -5

x \geq 5

Solve the equation:

5-3x ≤ -10

Move the constant term, 5, to the right side by subtracting 5 from both sides of the inequality:

5-3x-5 ≤ -10-5

-3x \leq -15

Divide both sides of the inequality by -3, and switch the direction of the inequality as -3 is negative:

\dfrac {-3x} {- 3} \geq \dfrac {-15} {- 3}

x \geq 5

The set of solutions is \left[ 5,+\infty \right).

4x-3 ≤ 9

x \geq 2

x \leq 5

x\leq 4

x\leq 3

Solve the equation:

4x-3 ≤ 9

Move the constant term, -3, to the right side by adding 3 to both sides of the inequality:

4x-3+3 ≤ 9+3

4x \leq 12

Divide both sides of the inequality by 4.

\dfrac {4x} {4} \leq \dfrac {12} {4}

x \leq 3

The set of solutions is \left(-\infty,3\right].

7x-3 \leq 11

x\leq2

x \geq 1

x \leq 4

x\leq -3

Solve the equation:

7x-3 \leq 11

Move the constant term, -3, to the right side by adding 3 to both sides of the inequality:

7x-3 +3 \leq 11 +3

7x \leq 14

Divide both sides of the inequality by 7.

\dfrac {7x} {7} \leq \dfrac {14} {7}

x \leq 2

The set of solutions is \left(-\infty,2\right].

3-2x \geq -5

x \geq 4

x \geq -4

x \leq -4

x \leq 4

Solve the equation:

3-2x \geq -5

Move the constant term, 3, to the right side by subtracting 3 from both sides of the inequality:

3-2x-3 \geq -5-3

-2x \geq -8

Divide both sides of the inequality by -2, and switch the direction of the inequality as -2 is negative:

\dfrac {-2x} {- 2} \geq \dfrac {-8} {- 2}

x \leq 4

The set of solutions is \left(-\infty,4\right].

2x+1 \leq 6

x\geq \dfrac{3}{2}

x \geq \dfrac{5}{2}

x \leq \dfrac{5}{2}

x \leq \dfrac{3}{2}

Solve the equation:

2x+1 \leq 6

Move the constant term, 1, to the right side by subtracting 1 from both sides of the inequality:

2x+1 -1 \leq 6-1

2x \leq 5

Divide both sides of the inequality by 2:

\dfrac {2x} {2} \leq \dfrac {5} {2}

x \leq \dfrac{5}{2}

The set of solutions is \left(-\infty,\dfrac{5}{2}\right].

5-2x \leq 10

x\geq \dfrac{5}{2}

x \leq \dfrac{5}{2}

x \geq \dfrac{-5}{2}.

x \leq \dfrac {-5} {2}

Solve the equation:

5-2x \leq 10

Move the constant term, 5, to the right side by subtracting 5 from both sides of the inequality:

5-2x -5 \leq 10 -5

-2x \leq 5

Divide both sides of the inequality by -2, and switch the direction of the inequality as -2 is negative:

\dfrac {-2x} {- 2} \geq \dfrac {5} {- 2}

x \geq \dfrac{-5}{2}

The set of solutions is \left[-\dfrac{5}{2},+\infty\right).