Virginia SOL Math / Algebra I / Equations & Inequalities

A.EI.1

Multistep & Literal Equations

What you'll learn

  • Solve multistep linear equations in one variable
  • Solve and graph linear inequalities in one variable
  • Solve literal equations for a specified variable

Words to know

Equation —
a statement that two expressions are equal
Inequality —
a comparison using <, >, <=, or >=
Literal equation —
an equation with several variables, like a formula
Inverse operation —
the operation that undoes another
Solution —
a value that makes the equation or inequality true
Coefficient —
the number multiplied by the variable

Why it matters Solving equations is how we work backward from a result to the unknown that produced it, and literal equations let us rearrange any formula.

Worked examples

Model ItI do

Solve 2x + 3 = 11.

Subtract 3 from both sides: 2x = 8. Then divide both sides by 2: x = 4. The balance stays level at each step.

Try It TogetherWe do

Solve 3(x - 2) = 12.

Distribute: 3x - 6 = 12. Add 6 to both sides: 3x = 18. Divide by 3: x = 6.

Now YouYou do

Solve the literal equation A = l * w for w.

Divide both sides by the factor that multiplies w. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Solve: x + 6 = 10.

  2. 2.Solve: 3x = 15.

  3. 3.Solve the inequality: x - 2 > 3.

On Level

The core Quick Check from the book.

  1. 1.Solve: 4x - 5 = 19.

  2. 2.Solve: 2(x + 3) = 14.

  3. 3.Solve the inequality: x + 4 > 9.

  4. 4.Solve for r: d = r * t.

  5. 5.Solve: (x / 3) + 1 = 5.

Challenge

Stretch your thinking.

  1. 1.Solve: 3(x - 4) = 2x + 1.

  2. 2.Solve for h: A = (1/2) * b * h.

  3. 3.Solve: (2x - 1) / 3 = 5.