Problem:
The given task involves solving the linear equation:
\[
4x + 3 = 2x + 5
\]
Let's solve this step by step and verify the solution.
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####
Step 1: Write down the given equation
\[
4x + 3 = 2x + 5
\]
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####
Step 2: Isolate the variable terms on one side
To do this, subtract \(2x\) from both sides of the equation:
\[
4x + 3 - 2x = 2x + 5 - 2x
\]
Simplify both sides:
\[
(4x - 2x) + 3 = 5
\]
\[
2x + 3 = 5
\]
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####
Step 3: Isolate the constant terms on the other side
Subtract 3 from both sides of the equation:
\[
2x + 3 - 3 = 5 - 3
\]
Simplify both sides:
\[
2x = 2
\]
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####
Step 4: Solve for \(x\)
Divide both sides of the equation by 2:
\[
\frac{2x}{2} = \frac{2}{2}
\]
Simplify:
\[
x = 1
\]
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####
Step 5: Verify the solution
To ensure the solution is correct, substitute \(x = 1\) back into the original equation:
\[
4x + 3 = 2x + 5
\]
Substitute \(x = 1\):
\[
4(1) + 3 = 2(1) + 5
\]
Simplify both sides:
\[
4 + 3 = 2 + 5
\]
\[
7 = 7
\]
Since both sides are equal, the solution is verified.
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Final Answer:
\[
\boxed{x = 1}
\]
Parent Tip: Review the logic above to help your child master the concept of solving equations combining like terms worksheet.
