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SAT Math skill page

SAT Linear Equations Practice

Build the SAT Math skill behind one-variable equations, slope-intercept form, systems, and equation word problems.

Practice linear equations in Dolphin Try examples
12-18 min practice time 3 examples on page Heart of Algebra
Practice time 12-18 min
On-page examples 3 examples
Best for Heart of Algebra

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

If 3x + 5 = 20, what is the value of x?

  1. 3
  2. 4
  3. 5
  4. 6
Show answer and explanation

Answer: 5

Subtract 5 from both sides to get 3x = 15. Divide by 3, so x = 5.

Example 2 Medium

A line has equation y = 4x - 7. What is the y-value when x = 3?

  1. 5
  2. 8
  3. 12
  4. 19
Show answer and explanation

Answer: 5

Substitute x = 3 into y = 4x - 7. That gives y = 4(3) - 7 = 12 - 7 = 5.

Example 3 Hard

A tutor charges a fixed signup fee plus $18 per hour. A 5-hour session costs $115. What is the fixed signup fee?

  1. $15
  2. $25
  3. $35
  4. $90
Show answer and explanation

Answer: $25

Let f be the fixed fee. The total cost is f + 18h. For 5 hours, f + 18(5) = 115, so f + 90 = 115 and f = 25.

Avoid these traps

Common mistakes on this skill

Doing operations on only one side

Every addition, subtraction, multiplication, or division step has to preserve equality on both sides of the equation.

Solving for the wrong variable

SAT questions often ask for a value like 2x, x + 3, or the y-value, not always x itself.

Missing negative signs

Negative constants and negative slopes are common traps. Rewrite the equation slowly before solving.

Study plan

How to practice this skill in Dolphin

  1. Start by isolating the variable in one-variable equations.
  2. Move to slope-intercept questions and practice substituting x-values.
  3. Translate word problems into equations before touching the answer choices.
  4. Review missed questions by naming the exact algebra step that went wrong.
Practice linear equations in Dolphin

Related practice

Build the surrounding skills

SAT Systems of Equations PracticeSAT Linear Functions PracticeSAT Quadratic Equations PracticeSAT Math skill hub

FAQ

Questions about SAT Linear Equations Practice

How common are linear equations on SAT Math?

Linear equations show up often because they connect to algebra, word problems, graphs, systems, and function notation.

What should I practice after linear equations?

Move into systems of equations, functions, and algebra word problems so the same equation skills transfer into harder formats.

Can Dolphin give me more linear equation practice?

Yes. Dolphin can filter SAT practice by topic, track missed questions, and keep surfacing the algebra work that needs review.