Modulus equations and inequalities · Short practice

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Recall

Linear modulus graphs and inequalities — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = 4 \left|{x - 17}\right| + 1\). Here \(\displaystyle a=4, h=17, k=1, d=2\).

Find the x-coordinate of the vertex.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Linear modulus graphs and inequalities — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = \left|{x - 18}\right| + 2\). Here \(\displaystyle a=1, h=18, k=2, d=3\).

Find the x-coordinate of the vertex.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Method

Linear modulus graphs and inequalities — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = \left|{x - 18}\right| + 2\). Here \(\displaystyle a=1, h=18, k=2, d=3\).

Find the least value of f.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Linear modulus graphs and inequalities — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 \left|{x - 19}\right| + 3\). Here \(\displaystyle a=2, h=19, k=3, d=4\).

Find the least value of f.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Apply

Two modulus expressions — objective 3

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(4 x + 18\) and \(\displaystyle V=\)\(6 x + 37\). Consider \(\left|{4 x + 18}\right| = \left|{6 x + 37}\right|\).

Find the distance between the two solutions.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Two modulus expressions — objective 3

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(2 x + 19\) and \(\displaystyle V=\)\(4 x + 39\). Consider \(\left|{2 x + 19}\right| = \left|{4 x + 39}\right|\).

Find the distance between the two solutions.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Check understanding

Two modulus expressions — objective 4

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(2 x + 19\) and \(\displaystyle V=\)\(4 x + 39\). Consider \(\left|{2 x + 19}\right| = \left|{4 x + 39}\right|\).

Find the midpoint of the two solutions.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Two modulus expressions — objective 4

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(3 x + 20\) and \(\displaystyle V=\)\(5 x + 41\). Consider \(\left|{3 x + 20}\right| = \left|{5 x + 41}\right|\).

Find the midpoint of the two solutions.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

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