2.1: Multi-Step Equations | Algebra 1 Honors

How it works

An equation asserts equal values. Applying the same reversible operation to both sides preserves its solution set. Distribute and combine like terms before isolating the variable. After solving, substitute into the original equation, particularly when negative signs appear.

a=b\ \Longrightarrow\ a+c=b+c

Worked examples

Example 1

Solve $\displaystyle 3(x-2)+4=16$ .

Distribute: $\displaystyle 3x-6+4=16$ . Thus $\displaystyle 3x=18$ and $\displaystyle x=6$ . Check: $\displaystyle 3(6-2)+4=16$ .

Example 2

Solve $\displaystyle 5x+2=2x+14$ .

Subtract $\displaystyle 2x$ and $\displaystyle 2$ : $\displaystyle 3x=12$ . Therefore $\displaystyle x=4$ .

Problems

Problem 2.1.1

Solve $\displaystyle 4(x+1)-3=13$ .

Show worked solution

$\displaystyle 4x+1=13$ , so $\displaystyle 4x=12$ and $\displaystyle x=3$ .

Problem 2.1.2

Solve $\displaystyle 7-2x=19$ .

Show worked solution

$\displaystyle -2x=12$ , so $\displaystyle x=-6$ . Check: $\displaystyle 7-2(-6)=19$ .

Problem 2.1.3

Solve $\displaystyle 2(x+3)=2x+6$ .

Show worked solution

Both sides simplify to $\displaystyle 2x+6$ , so every real number is a solution.

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 2.1.1

Problem 2.1.2

Problem 2.1.3

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