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

Score band 500-600 · Heart of Algebra

Absolute Value Equations drills for 500-600

400500600700800

Targeted practice for students currently scoring in the 500-600 range, drilling exclusively on absolute value equations.

What a 500-600 scorer needs from this topic

The 500 to 600 score band is where most students start when they first sit a practice SAT. Questions in this band still test single concepts, but the numbers get less friendly and the stems get longer. The College Board starts adding distractors that punish students who solved correctly but answered the wrong question. To break out of this band, you need to combine accuracy on the easy questions with a willingness to slow down on the medium ones. Building-band drills focus on the most common medium-difficulty patterns released by the College Board: word-problem translation, multi-step arithmetic, two-variable systems with messy coefficients, and proportional reasoning with awkward unit conversions.

For Absolute Value Equations specifically, students in the 500-600 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 500-600 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. 500-600 easy Distance Interpretation of Absolute Value

    If |4x - 10| = 2, what is the sum of all values of x that satisfy the equation?

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

    Answer: C — 5

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 4x + (-10) = 2 gives x = 3. Case 2: 4x + (-10) = -2 gives x = 2. Sum = 3 + (2) = 5.

  2. 500-600 easy Graphing Absolute Value Functions

    If |1x - 9| = 8, what is the sum of all values of x that satisfy the equation?

    1. A 18
    2. B 17
    3. C 1
    4. D 16
    Worked solution

    Answer: A — 18

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 1x + (-9) = 8 gives x = 17. Case 2: 1x + (-9) = -8 gives x = 1. Sum = 17 + (1) = 18.

  3. 500-600 medium Solving Basic Absolute Value Equations

    If |3x + 6| = 15, what is the sum of all values of x that satisfy the equation?

    1. A -4
    2. B -7
    3. C 10
    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: 3x + (6) = 15 gives x = 3. Case 2: 3x + (6) = -15 gives x = -7. Sum = 3 + (-7) = -4.

  4. 500-600 medium Absolute Value Inequalities

    If |4x + 2| = 14, 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 + (2) = 14 gives x = 3. Case 2: 4x + (2) = -14 gives x = -4. Sum = 3 + (-4) = -1.

  5. 500-600 medium Distance Interpretation of Absolute Value

    If |4x - 10| = 2, what is the sum of all values of x that satisfy the equation?

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

    Answer: C — 5

    An absolute-value equation |u| = c with c > 0 splits into two cases: u = c and u = -c. Case 1: 4x + (-10) = 2 gives x = 3. Case 2: 4x + (-10) = -2 gives x = 2. Sum = 3 + (2) = 5.

  6. 500-600 medium Graphing Absolute Value Functions

    If |4x - 1| = 11, what is the sum of all values of x that satisfy the equation?

    1. A -2
    2. B 1
    3. C 5
    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 + (-1) = 11 gives x = 3. Case 2: 4x + (-1) = -11 gives x = -2. Sum = 3 + (-2) = 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 500-600 drills