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Great question! Let's solve this linear equation step by step.

We are given: 3(x − 2) + 4 = 19.

Step 1: Apply the distributive property.

The distributive property states that a(b + c) = ab + ac.

So 3(x − 2) = 3x − 6, and the equation becomes 3x − 6 + 4 = 19.

Step 2: Combine like terms on the left side.

Since −6 + 4 = −2, we get 3x − 2 = 19.

Step 3: Isolate the variable term by adding 2 to both sides.

3x − 2 + 2 = 19 + 2, which simplifies to 3x = 21.

Step 4: Divide both sides by 3 to solve for x.

3x ÷ 3 = 21 ÷ 3, so x = 7.

Step 5: Verify the solution by substituting x = 7 back in.

3(7 − 2) + 4 = 3(5) + 4 = 15 + 4 = 19 ✓

So the solution is x = 7. Want more practice problems?