1) Solve for \(x\): \(2x+5=3x-7\).
2) Solve for \(y\): \(3y+7-12y>5y-8\).
3) Solve for \(x\): \( -(2x-5)=13-4x \).
4) Solve for \(y\): \( -3(2y+1) < 4y-3\).
5) Solve for \(x\): \( -\Large\frac{7}{2}\normalsize x+13=\Large\frac{1}{2}\normalsize (-x+2) \).
6) Solve for \(x\): \( 2\left(x+\Large\frac{7}{2}\right)=\normalsize (x+3)+(x+4) \).
7) Solve for \(y\): \( \Large\frac{3}{2}\normalsize y-5 \leq 45- \Large\frac{7}{2}\normalsize y \).
8) Solve for \(y\): \( 7y-(5y-12)=20+2y+4 \).
2) Solve for \(y\): \(3y+7-12y>5y-8\).
3) Solve for \(x\): \( -(2x-5)=13-4x \).
4) Solve for \(y\): \( -3(2y+1) < 4y-3\).
5) Solve for \(x\): \( -\Large\frac{7}{2}\normalsize x+13=\Large\frac{1}{2}\normalsize (-x+2) \).
6) Solve for \(x\): \( 2\left(x+\Large\frac{7}{2}\right)=\normalsize (x+3)+(x+4) \).
7) Solve for \(y\): \( \Large\frac{3}{2}\normalsize y-5 \leq 45- \Large\frac{7}{2}\normalsize y \).
8) Solve for \(y\): \( 7y-(5y-12)=20+2y+4 \).
For #9-10 drag the red circles onto the blue circles and see if you can identify the correct justifications for each step.
9)
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10)
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Looking at the work below, justify each step.
11)
\( \begin{align*} 3x+7y &= 12 \\ 7y &=-3x+12 \\ y&=-\frac{3}{7}x+\frac{12}{7} \end{align*} \)
12)
\( \begin{align*} -5x-7y+12x &= 10+2y \\ 7x-7y &= 10+2y \\ 7x-9y &= 10 \\ -9y &= 10-7x \\ y&= \frac{10-7x}{-9} \end{align*} \)
13)
\( \begin{align*} \frac{3x}{5} &= \frac{11y}{10} \\ 3x &= \frac{11y}{2} \\ x &= \frac{11y}{6} \end{align*} \)
14)
\( \begin{align*} -(5x+2) &= 12y +x \\ -5x-2 &= 12y +x \\ -6x-2 &= 12y \\ 12y &= -6x-2 \\ y&= -\frac{1}{2} x - \frac{1}{6} \end{align*} \)
Solution Bank
11)
\( \begin{align*} 3x+7y &= 12 \\ 7y &=-3x+12 \\ y&=-\frac{3}{7}x+\frac{12}{7} \end{align*} \)
12)
\( \begin{align*} -5x-7y+12x &= 10+2y \\ 7x-7y &= 10+2y \\ 7x-9y &= 10 \\ -9y &= 10-7x \\ y&= \frac{10-7x}{-9} \end{align*} \)
13)
\( \begin{align*} \frac{3x}{5} &= \frac{11y}{10} \\ 3x &= \frac{11y}{2} \\ x &= \frac{11y}{6} \end{align*} \)
14)
\( \begin{align*} -(5x+2) &= 12y +x \\ -5x-2 &= 12y +x \\ -6x-2 &= 12y \\ 12y &= -6x-2 \\ y&= -\frac{1}{2} x - \frac{1}{6} \end{align*} \)
Solution Bank