1) \(4L\) of a \(7\%\) of salt solution is needed for an experiment. To create this, a scientist must mix a \(12\%\) salt solution with a \(5\%\) salt solution. How much of the \(5\%\) salt solution is needed?
2) Solve for \(x\) when \(y\) is negative: \(5y-7xy\ge 13-3x\).
3) When the linear equation \(3y-5x+2=-4(x-y)+13\) is written in slope-intercept form, \(y=Ax+B\) where \(A\) and \(B\) are real numbers, find the sum of \(A\) and \(B\).
4) Solve for \(y\): \({\dfrac{4xy+7}{y}}\normalsize+3x-4=2x\)
5) Solve: \(2\left( y+2 \right)+{\dfrac{y+1}{3}=\dfrac{1}{6}}\normalsize\left( 2-y \right)-4y\)
6) Two siblings are biking towards school from the same house. One sibling is on a road bike and bikes \(6\) mph faster than her sibling on a mountain bike. They both leave at 7:00 am. The sibling on the road bike arrives at school at 7:30 am and the mountain biker arrives at 7:40 am. What is the speed of the faster biker? How far do they live from the school?
7) Find \(k\) such that \(3x-4y=7\) and \(kx +8y= 9\) are parallel.
8) If \(4x+2= A(x-1)+B(x+1)\) for all \(x \in \mathbb{R} \) then find the values of \(A\) and \(B\).
9) Let \(u=5x^2+3\), find \( (5x^2 + 5)^2 -10x^2-6 \) in terms of \(u\).
10) Suppose that \(y\) varies linearly with \(x\). If \(y=8\) when \(x=2\) and \(y=-3\) when \(x=4\), then find the value of \(x\) when \(y= 52\).
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2) Solve for \(x\) when \(y\) is negative: \(5y-7xy\ge 13-3x\).
3) When the linear equation \(3y-5x+2=-4(x-y)+13\) is written in slope-intercept form, \(y=Ax+B\) where \(A\) and \(B\) are real numbers, find the sum of \(A\) and \(B\).
4) Solve for \(y\): \({\dfrac{4xy+7}{y}}\normalsize+3x-4=2x\)
5) Solve: \(2\left( y+2 \right)+{\dfrac{y+1}{3}=\dfrac{1}{6}}\normalsize\left( 2-y \right)-4y\)
6) Two siblings are biking towards school from the same house. One sibling is on a road bike and bikes \(6\) mph faster than her sibling on a mountain bike. They both leave at 7:00 am. The sibling on the road bike arrives at school at 7:30 am and the mountain biker arrives at 7:40 am. What is the speed of the faster biker? How far do they live from the school?
7) Find \(k\) such that \(3x-4y=7\) and \(kx +8y= 9\) are parallel.
8) If \(4x+2= A(x-1)+B(x+1)\) for all \(x \in \mathbb{R} \) then find the values of \(A\) and \(B\).
9) Let \(u=5x^2+3\), find \( (5x^2 + 5)^2 -10x^2-6 \) in terms of \(u\).
10) Suppose that \(y\) varies linearly with \(x\). If \(y=8\) when \(x=2\) and \(y=-3\) when \(x=4\), then find the value of \(x\) when \(y= 52\).
Solution Bank