Solving equations with variables on both sides is a part of algebra 1 (second math course) syllabus. For solving equations with fractions and variables, multiply every term by the denominators, so that fractions are cleared out. Then it reduces to solving equations with variables on each side. Next group all the like terms on one side by adding or subtracting the same value on both sides. Then the problem becomes a system of linear equations.This can be solved by the standard method. Practice many problems from linear equations worksheet and learn more about solving algebra equations using the resources on this page.
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But for now, here is how to solve the question in the above example using inverses:
First, write down the expression:
2a + 3 = 7.
Then, undo the + 3 by subtracting 3. Remember, you need to do it to BOTH sides!
2a + 3 – 3 = 7 – 3,
so 2a = 4.
Undo the multiply by 2 by dividing by 2, again on both sides:
2a ÷ 2 = 4 ÷ 2.
To solve an equation like this, you must first get the variables on the same side of the equal sign. Add -2.5y to both sides so that the variable remains on one side only. Now isolate the variable by subtracting 10.5 from both sides. Multiply both sides by 10 so that 0.5y becomes 5y, then divide by 5.
Method 1 Using the Substitution Method**Move the variables to different sides of the equation. … **Divide both sides of the equation to “solve for x.” … **Plug this back into the other equation. … **Solve for the remaining variable. … **Use the answer to solve for the other variable. … **Know what to do when both variables cancel out.
But for now, here is how to solve the question in the above example using inverses:**First, write down the expression:**2a + 3 = 7.**Then, undo the + 3 by subtracting 3. Remember, you need to do it to BOTH sides!**2a + 3 – 3 = 7 – 3,**so 2a = 4.**Undo the multiply by 2 by dividing by 2, again on both sides:**2a ÷ 2 = 4 ÷ 2.