Lesson

 

Problems & Videos

Solve for x.

\(\textbf{1)}\) \( 3x+5=7x-3 \)

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The answer is \( x=2 \)

 

\(\textbf{2)}\) \( 4x=2x \)

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The answer is \( x=0 \)

 

\(\textbf{3)}\) \( x+2=x-3 \)

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The answer is No solution

 

\(\textbf{4)}\) \( x+5=x+5 \)

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The answer is All Real Numbers

 

\(\textbf{5)}\) \( 5x-7=10x+8 \)

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The answer is \( x=-3 \)

 

\(\textbf{6)}\) \( 3x=2x+5 \)

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The answer is \( x=5 \)

 

\(\textbf{7)}\) \( 5x+1=3x+5 \)

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The answer is \( x=2 \)

 

Challenge Problems

\(\textbf{8)}\) \(−10 + 5x = x − 3 − 3x\)

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The answer is \(x = 1 \,\,\,\)

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\(−10 + 5x = x − 3 − 3x \,\,\,\) (Starting Problem)
\(−10 + 5x = -2x − 3 \,\,\,\) (Simplify)
\(−10 + 7x = − 3 \,\,\,\) (Add 2x to both sides)
\(7x = 7 \,\,\,\) (Add 10 to both sides)
\(x = 1 \,\,\,\) (Divide both sides by 7)

 

\(\textbf{9)}\) What value of the constant \(a\) does the equation have infinitely many solutions? \(5x+3=(a-2)x+3\)

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The answer is \(a=7\)

 

See Related Pages\(\)

\(\bullet\text{ Solving Equations by Addition and Subtraction}\)
\(\,\,\,\,\,\,\,\,x+3=4…\)

\(\bullet\text{ Solving Equations by Multiplication and Division}\)
\(\,\,\,\,\,\,\,\,8x=48…\)

\(\bullet\text{ Solving Multi-step Equations}\)
\(\,\,\,\,\,\,\,\,3x+2=14…\)

\(\bullet\text{ Solving Equations with Variables on Both Sides}\)
\(\,\,\,\,\,\,\,\,3x+5=7x-3…\)

\(\bullet\text{ Solving Equations with Decimals}\)
\(\,\,\,\,\,\,\,\,43.5+0.2x=51.1…\)

\(\bullet\text{ Solving Equations with Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}…\)