help_outline Original Question
Solve for x: 5x + 3 = 23
summarize Solution Overview
This problem asks us to find the value of x in a basic algebraic equation. To solve it, we will use inverse operations to isolate x on one side of the equals sign. We'll start by removing the constant (+3) and then dividing by the coefficient (5).
Final Answer
format_list_numbered Step-by-Step Solution
1.
Isolate the
variable term
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To solve for x, we first need to get the term with x (which is 5x) by itself. Subtract 3 from both sides of the equation.
5x = 20
2.
Solve for
x
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Now we need to find what 1x is. Since x is multiplied by 5, divide both sides by 5.
x = 4
functions Formula Explanation
Equation Form: ax + b = c
Where a is the coefficient, x is the variable, b is the constant, and c is the result.
This is a basic linear equation solved using inverse operations.
history_edu Formula Derivation
If ax + b = c, then:
ax = c - b
x = (c - b) / a
psychology Logical Reasoning Breakdown
lightbulb The "Why"
Inverse operations undo actions. Subtraction undos addition.
balance Balance
The equals sign is a promise of balance. Both sides must change equally.
school Concept Clarity
Think of an equation as a perfectly balanced scale. To keep it level, every weight added or removed from one side must be matched on the other.
error_outline Common Mistake
Forgetting to divide the right side. Don't just "cancel" the 5 on the left; you must actually perform the division on the 20 as well.
edit_note Practice Question
Solve for y: 4y - 7 = 25