Solve for x practice that opens the door to algebra

Free, no-login solve-for-x drills. One-step and two-step equations, integer solutions, including negatives at higher levels. Best for 6th and 7th grade.

“Solve for x” is the first algebraic move most kids meet. The arithmetic underneath is just 4th- and 5th-grade operations — what’s new is the structure: instead of asking “what does this equal,” the equation asks “what value of x makes this true?” That shift is the gateway to algebra. This page is specifically about getting that move automatic. For the broader pre-algebra track see the pre-algebra practice page.

What “solve for x” means in 6th and 7th grade

Most 6th-grade and 7th-grade equations come in two forms:

One-step equations (CCSS 6.EE.B.7)

• x + b = c (add or subtract to isolate x). Example: x + 7 = 12 → x = 5.
• ax = c (multiply or divide to isolate x). Example: 3x = 21 → x = 7.

Two-step equations (CCSS 7.EE.B.4)

• ax + b = c. Example: 3x + 5 = 17 → subtract 5 from both sides → 3x = 12 → divide by 3 → x = 4.
• With negative coefficients or constants: −2x + 9 = 15 → −2x = 6 → x = −3.

The Num Drill levels for solve-for-x

All six levels of pre-algebra are solve-for-x problems, progressively harder:

• Levels 1–2: One-step equations, positive integer solutions.
• Levels 3–4: Two-step equations, positive integer solutions, including negative coefficients/constants.
• Levels 5–6: Two-step equations, integer solutions including negatives.

The two skills hidden in solve-for-x

Most kids who struggle with “solve for x” aren’t struggling with the algebra; they’re struggling with the arithmetic the algebra requires. Two underlying skills decide success:

1. Inverse arithmetic. “What times 3 is 21?” is just multiplication-fact recall in disguise. Kids without fluent multiplication facts stall on every one-step equation.
2. Integer arithmetic. −2x + 9 = 15 requires “15 − 9 = 6” followed by “6 ÷ (−2) = −3.” Both moves are operations on signed integers — a separate skill kids don’t fully consolidate until 6th grade.

If your child stalls on solve-for-x problems and you can’t tell why, run a multiplication-facts diagnostic. Most stalls trace back there.

The standard 4-week solve-for-x routine

• Week 1: Pre-algebra level 1 daily. One-step equations only. Focus on identifying which inverse operation to apply.
• Week 2: Pre-algebra level 2. Same shape, larger numbers. Speed up.
• Week 3: Pre-algebra level 3. Two-step equations, positive only. Most kids feel a real cognitive jump here — the two-step plan is new.
• Week 4: Pre-algebra level 4. Two-step with negatives. The 7th-grade level.

What to do when your child guesses

Some kids try to solve x + 7 = 12 by guessing values of x and checking. That works on tiny numbers but breaks immediately on anything harder. The fix isn’t to ban guessing; it’s to drill at the right level (where guessing is too slow to be viable) and let the procedure win because it’s faster. Per-question timing in Num Drill makes this transparent — kids who guess take 15–30 seconds per question; kids using the procedure take 4–8 seconds.

Related reading: pre-algebra practice · multiplication practice · 6th grade math practice