Solving more complicated linear inequalities | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these shows the solutions to the inequality $3<2x+1$ ?

$x<1$

$x>1$ ✓

$x<2$

$x>2$
The solution to $\frac{x+5}{3} \ge 3$ is when $x \ge$ ______

'4' ✓
Which of these values satisfy the inequality $3 < x \le 4$ ?

$x=2.5$

$x=3$

$x=3.5$ ✓

$x=4$ ✓

$x=4.5$
Which of these values satisfy the inequality $-3 < x < -2$ ?

$x=-3$

$x=-2$

$x=-3.5$

$x=-2.5$ ✓

$x=-1.5$
If $-x > 3$ which of the following is an equivalent inequality?

$x<3$

$x<-3$ ✓

$x>3$

$x>-3$
Which inequality represents all values which satisfy both of the drawn inequalities?

$4 < x \le 6$

$x > 4$

$x \ge 4$

$x > 6$

$x \ge 6$ ✓

Which of these shows all solutions to the inequality $19<2x+3 \le 21$ ?

$7 < x \le 9$

$8 < x \le 9$ ✓

$8 < x \le 12$

$9 < x \le 11$

$11 < x \le 12$
Which of these shows all solutions to the inequality $-2 < -x < 1$ ?

$-2 < x < -1$

$-2 < x < 1$

$-1 < x < 2$ ✓

$1 < x < 2$
Which of these represents all values which satisfy both $x>3$ and $4 ?$

$x>3$

$x<4$

$x>4$ ✓

$3$

$x<3$ or $x>4$
What are the solutions to the inequality $x+1<3x+1 ?$

$-3 < x < 0$

$0< x < 3$ ✓

$1 < x < 3$

$1 < x < 6$
Which is the correct way to separate $3x+2 \le 4x+3 \le 2x+9$ into two inequalities to solve?

$3x + 2 \le 4x$ and $3 \le 2x + 9$

$3x + 2 \le 4x + 3$ and $4x + 3 \le 2x + 9$ ✓

$4x+1 \ge 3x+2$ and $4x+3 \ge 2x+9$

$3x+2 \le 4x+3$ and $3x+2 \le 2x+9$
Solve the inequality $3x+2 \le 4x+3 \le 2x+9$ .

$-1 \le x \le 3$ ✓

$-1 \le x \le 6$

$1 \le x \le 3$

$1 \le x \le 6$

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Inequalities can be combined to be more efficient
By treating the combined inequality as two separate inequalities, you can easily solve
There may be a set of possible values, inequality notation can be used to communicate them efficiently

Dividing or multiplying by -1 does not change the inequality sign.

2 < 3 becomes -2 > -3 when both sides are multiplied by -1.

Inequality - An inequality is used to show that one expression may not be equal to another.