ACT Algebra: Complete Guide to Equations, Inequalities & Systems

ACT says Algebra accounts for roughly 17–20% of current ACT Math.

Algebra is also the language used inside many other questions.

That makes it one of the highest-value areas to make automatic.

For the full breakdown of everything tested on ACT Math, see the Enhanced ACT guide — and the rest of our ACT guides cover every other section too. If you're mapping out when to sit for the exam, check the ACT test dates for upcoming registration windows.

Linear equations

Solve:

[ 4x-7=21 ]

[ 4x=28 ]

[ x=7 ]

Variables on both sides

[ 5x+2=2x+20 ]

[ 3x=18 ]

[ x=6 ]

Inequalities

[ 3x-4>11 ]

[ 3x>15 ]

[ x>5 ]

If you multiply or divide by a negative number, reverse the inequality sign.

Systems

[ x+y=10 ]

[ x-y=4 ]

Add:

[ 2x=14 ]

[ x=7,\quad y=3 ]

Expressions

Expand:

[ 3(x+5)-2x ]

[ 3x+15-2x=x+15 ]

Factoring

[ x^2+7x+12 ]

[ (x+3)(x+4) ]

Absolute value

[ |x-2|=5 ]

Two cases:

[ x-2=5 ]

or

[ x-2=-5 ]

So:

[ x=7\quad\text{or}\quad x=-3 ]

Word problems

Translate phrases carefully.

“Seven more than twice x”:

[ 2x+7 ]

“Seven times the sum of x and 2”:

[ 7(x+2) ]

Not the same.

Original practice

1

Solve:

[ 6x+5=29 ]

2

Solve:

[ 2x+9=5x-6 ]

3

Solve:

[ -3x<12 ]

4

Solve the system:

[ x+y=9 ] [ x-y=1 ]

5

Solve:

[ |x+1|=4 ]

Answers

1. 4
2. 5
3. x > -4
4. x=5, y=4
5. 3 or -5

Common traps

• sign mistakes;
• forgetting inequality reversal;
• distributing only to the first term;
• translating word problems incorrectly;
• losing the second absolute-value solution.

Which of these traps costs you the most matters more once you've set a target — see what counts as a good ACT score to figure out yours.

Bottom line

ACT Algebra rewards reliable basics.

At high speed, small algebra mistakes become expensive.

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