Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?

Practice Problems

\(\textbf{1)}\) \(\text{Solve for }k. \,\, A=\frac{1}{2}h(b+k)\)

Show Answer

The answer is \(k=\displaystyle\frac{2A}{h}-b, \,\,\, h\ne 0 \)

Show Work

\(\,\,\,\,\,A=\frac{1}{2}h(b+k)\)

\(\,\,\,\,\,2A=h(b+k)\)

\(\,\,\,\,\,\displaystyle\frac{2A}{h}=(b+k) \,\,\, h\ne 0\)

\(\,\,\,\,\,\displaystyle\frac{2A}{h}-b=k \,\,\, h\ne 0\)

\(\,\,\,\,\,k = \displaystyle\frac{2A}{h}-b \,\,\, h\ne 0\)

\(\textbf{2)}\) \(\text{Solve for }C. \,\, F=\frac{9}{5}C+32\)

Show Answer

The answer is \(C=\frac{5}{9}(F-32)\)

\(\textbf{3)}\) \(\text{Solve for }b. \,\, A=\frac{1}{2}bh\)

Show Answer

The answer is \(b=\frac{2A}{h}, \,\,\, h\ne 0\)

\(\textbf{4)}\) \(\text{Solve for }x. \,\, y=3x+5\)

Show Answer

The answer is \(x=\frac{y-5}{3}\)

\(\textbf{5)}\) \(\text{Solve for }m. \,\, R=2m-5\)

Show Answer

The answer is \(m=\frac{R+5}{2}\)

\(\textbf{6)}\) \(\text{Solve for }d. \,\, G=2d+3c\)

Show Answer

The answer is \(d=\frac{G-3c}{2}\)

\(\textbf{7)}\) \(\text{Solve for }s. \,\, F=\frac{1}{5}s-5\)

Show Answer

The answer is \(s=5F+25\)

\(\textbf{8)}\) \(\text{Solve for }j. \,\, w=3j+2h-32\)

Show Answer

The answer is \(j=\frac{w-2h+32}{3}\)

\(\textbf{9)}\) \(\text{Volume of a sphere: } V=\frac{4}{3} \pi r^3 \text{, solve for }r \)

Show Answer

The Answer is \( r=\sqrt[3]{\frac{3V}{4 \pi}} \)

\(\textbf{10)}\) \(\text{Area of a trapezoid: } A=\frac{1}{2} \left(b_1+b_2\right)h \text{, solve for }h \)

Show Answer

The Answer is \( h=\frac{2A}{b_1+b_2} \)

\(\textbf{11)}\) \(\text{Area of a trapezoid: } A=\frac{1}{2} \left(b_1+b_2\right)h \text{, solve for }b_1 \)

Show Answer

The Answer is \( b_1=\frac{2A}{h}-b_2 \)

\(\textbf{12)}\) \(\text{Area of a circle: } A=\pi r^2 \text{, solve for }r \)

Show Answer

The Answer is \( r=\sqrt{\frac{A}{\pi}} \)

\(\textbf{13)}\) \(\frac{a+b}{c+b}=2, \text{ solve for }b \)

Show Answer

The Answer is \( b=a-2c\)

\(\textbf{14)}\) \(m^2+bx^2=k, \text{ solve for }x \)

Show Answer

The Answer is \( x=\pm \sqrt{\frac{k-m^2}{b}}\)

Challenge Problems

\(\textbf{15)}\) \(\text{Solve for }y. \,\, hy+by=x\)

Show Answer

The answer is \(y=\frac{x}{h+b}, \,\,\, h\ne -b\)

Show Work

\(\,\,\,\,\,hy+by=x\,\,\,\left(\text{Given}\right)\)

\(\,\,\,\,\,y(h+b)=x\,\,\,\left(\text{Factor out a y}\right)\)

\(\,\,\,\,\,y=\frac{x}{h+b}\,\,\,\left(\text{divide both sides by (h+b)}\right)\)

The answer is \(y=\frac{x}{h+b}, \,\,\, h\ne -b\)

\(\textbf{16)}\) If \(\frac{x}{y}=3\) and \(xz+1=16\), then \(yz=\)

Show Answer

The answer is \(yz=5\)

\(\textbf{17)}\) If \(y=xz+x\). What is \( \displaystyle\frac{y}{x}\) ?

Show Answer

The answer is \(\frac{y}{x}=z+1, \,\,\, x\ne 0\)

\(\textbf{18)}\) If \(\frac{2}{x}=8\), then \(3x=\)

Show Answer

The answer is \(3x=\displaystyle\frac{3}{4}\)

\(\textbf{19)}\) If \(4p+3q=7b\), what is \(q\) in terms of \(b\) and \(p\)?

Show Answer

The answer is \(q=\displaystyle\frac{7b-4p}{3}\)

\(\textbf{20)}\) Solve for y,
\(zy+2=3y+x\)

Show Answer

The answer is \(y=\displaystyle\frac{x-2}{z-3}, \,\,\, z\ne 3\)

\(\textbf{21)}\) \(\text{Solve for }x. \,\, \frac{3(x-1)+2}{4x}=\frac{1-4x}{2x}+1\)

Show Answer

The answer is \(x=\frac{3}{7}\)

\(\textbf{22)}\) \(\text{Solve for }x. \,\, Ax-By=C\)

Show Answer

The answer is \(x=\frac{C+By}{A}, \,\,\, A\ne 0\)

\(\textbf{23)}\) \(\text{Solve for }x. \,\, ax-4c=5+bx\)

Show Answer

The answer is \(x=\frac{5+4c}{a-b}, \,\,\, a\ne b\)

\(\textbf{24)}\) \(\text{Solve for }y. \,\, \frac{2}{3}y+\frac{1}{2}x+7=-4\)

Show Answer

The answer is \(y=\frac{-3x-66}{4}\)

\(\textbf{25)}\) \(\text{Simplify } h(g-h)-g(h+1)+g(h+g)-(-h-g)+h\)

Show Answer

The answer is \(-h^2+gh+2h+g^2\)

\(\textbf{26)}\) \(\text{Simplify } 4x(x-2)-3x(4-x)\)

Show Answer

The answer is \(7x^2-20x\)

\(\textbf{27)}\) \(\text{Simplify } -5m^2+5m^2(3-4m)-m(m-8)-m\)

Show Answer

The answer is \(-20m^3+9m^2+7m\)

\(\textbf{28)}\) \(\text{Simplify } -(x-\frac{2}{3})-\frac{x}{3}-\frac{1}{3}(x-2)\)

Show Answer

The answer is \(\frac{-5x+4}{3}\)

See Related Pages\(\)

\(\bullet\text{ Fahrenheit and Celsius Conversions}\)
\(\,\,\,\,\,\,\,\,F=\frac{9}{5}C+32…\)

In Summary

To isolate a variable in an algebraic equation means to rewrite the equation in a form where the variable appears on one side of the equal sign and all the other terms appear on the other side. This is useful for solving equations and understanding the behavior of the variable.

To isolate a variable in an equation, you can use the basic operations of algebra, such as addition, subtraction, multiplication, and division. The specific steps you need to take will depend on the form of the equation and the variable you are trying to isolate.

Isolating a variable in an equation is an important concept in algebra, as it allows you to solve equations and understand the behavior of the variable.

About Andymath.com

Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.

Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.

Visit me on Youtube, Tiktok, Instagram and Facebook. Andymath content has a unique approach to presenting mathematics. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. We are open to collaborations of all types, please contact Andy at tutoring@andymath.com for all enquiries. To offer financial support, visit my Patreon page. Let’s help students understand the math way of thinking!

Thank you for visiting. How exciting!