ScoreReady SAT
Drill by score band: 400–500 500–600 600–700 700–800

Score band 400-500 · Heart of Algebra

Absolute Value Equations drills for 400-500

400500600700800

Targeted practice for students currently scoring in the 400-500 range, drilling exclusively on absolute value equations.

What a 400-500 scorer needs from this topic

The 400 to 500 score band on SAT Math is the foundations band. Students scoring here are usually strong on arithmetic but losing easy points to careless setup, missed units, or an unfamiliar SAT phrasing of a familiar idea. Drilling the foundations questions here is the highest leverage thing you can do for your score, because every problem you convert from a guess to a confident solve moves you a measurable number of scaled points. Foundations questions in this band test one idea at a time, with friendly numbers and short stems. Treat them as warmups for the rest of the section: do them untimed first, write every step on paper, and check that your final value answers the actual question being asked, not the value of x.

For Absolute Value Equations specifically, students in the 400-500 band need to focus on the question patterns the College Board uses at this difficulty level. Solve equations and inequalities involving absolute value. The questions below are pulled from the ScoreReady question bank and filtered to the 400-500 band based on difficulty calibration that matches publicly released College Board practice materials.

Drill these untimed first. Once you can produce a clean worked solution on paper for every question without notes, switch to timed mode and aim for under 75 seconds per question. That pace is roughly the average time per question on the actual SAT Math section, and it leaves time for the harder questions you will see at the end of each module.

Practice set

  1. 400-500 easy Solving Basic Absolute Value Equations

    If |2x - 4| = 2, what is the sum of all values of x that satisfy the equation?

    1. A 4
    2. B 1
    3. C 2
    4. D 3
    Worked solution

    Answer: A — 4

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 2x + (-4) = 2 gives x = 3. Case 2: 2x + (-4) = -2 gives x = 1. Sum = 3 + (1) = 4.

  2. 400-500 easy Absolute Value Inequalities

    If |2x - 6| = 4, what is the sum of all values of x that satisfy the equation?

    1. A 6
    2. B 4
    3. C 1
    4. D 5
    Worked solution

    Answer: A — 6

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 2x + (-6) = 4 gives x = 5. Case 2: 2x + (-6) = -4 gives x = 1. Sum = 5 + (1) = 6.

  3. 400-500 easy Distance Interpretation of Absolute Value

    If |1x - 4| = 17, what is the sum of all values of x that satisfy the equation?

    1. A 21
    2. B -13
    3. C 8
    4. D 34
    Worked solution

    Answer: C — 8

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 1x + (-4) = 17 gives x = 21. Case 2: 1x + (-4) = -17 gives x = -13. Sum = 21 + (-13) = 8.

  4. 400-500 easy Graphing Absolute Value Functions

    If |3x - 2| = 7, what is the sum of all values of x that satisfy the equation?

    1. A -1
    2. B 4
    3. C 2
    4. D 3
    Worked solution

    Answer: C — 2

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 3x + (-2) = 7 gives x = 3. Case 2: 3x + (-2) = -7 gives x = -1. Sum = 3 + (-1) = 2.

  5. 400-500 easy Solving Basic Absolute Value Equations

    If |3x + 0| = 9, what is the sum of all values of x that satisfy the equation?

    1. A 6
    2. B -3
    3. C 0
    4. D 3
    Worked solution

    Answer: C — 0

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 3x + (0) = 9 gives x = 3. Case 2: 3x + (0) = -9 gives x = -3. Sum = 3 + (-3) = 0.

  6. 400-500 easy Absolute Value Inequalities

    If |4x + 3| = 15, what is the sum of all values of x that satisfy the equation?

    1. A -4
    2. B -1
    3. C 7
    4. D 3
    Worked solution

    Answer: B — -1

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 4x + (3) = 15 gives x = 3. Case 2: 4x + (3) = -15 gives x = -4. Sum = 3 + (-4) = -1.

How to use these drills to climb a band

Climbing from one score band to the next requires a different study mix than climbing within a band. Within a band, you are mostly fixing careless errors and pattern-recognizing the question types you already understand. Climbing to the next band means adding new question types to your toolbox — patterns you currently recognize but cannot solve fluently. The 700–800 set in this drill is exactly that toolbox for students currently in the 600–700 range.

The single most reliable indicator that you are ready to move up a band is being able to explain a worked solution to someone else, in your own words, without referring to notes. Practice this with one classmate or one parent per week. The act of teaching exposes the gaps your timed solves did not.

Other 400-500 drills