For example, you might have the equation x−9=5{\displaystyle x-9=5}. The variable representing the unknown number is x{\displaystyle x}. When you subtract 9 from the unknown number, the difference is 5.
For example, in the equation x−9=5{\displaystyle x-9=5}, 9 is subtracted from the variable, so to isolate the variable you must cancel the 9 by adding it.
For example, in the equation x−9=5{\displaystyle x-9=5}, you need to add 9 to the left side to isolate the variable, so you also need to add 9 to the right side of the equation:x−9=5{\displaystyle x-9=5}x−9+9=5+9{\displaystyle x-9+9=5+9}x=14{\displaystyle x=14}.
For example, if you found that x=14{\displaystyle x=14}, substitute 14 for x{\displaystyle x} in the original equation: 14−9=5{\displaystyle 14-9=5}. Since this equation is true, your solution is correct.
For example, you might have the equation 3x=24{\displaystyle 3x=24}. The variable representing the unknown number is x{\displaystyle x}. When you multiply the unknown number and 3, the product is 24.
For example, in the equation 3x=24{\displaystyle 3x=24} the variable is multiplied by 3, so to isolate the variable you must cancel the 3 by dividing by 3.
For example, in the equation 3x=24{\displaystyle 3x=24}, you need to divide by 3 on the left side to isolate the variable, so you also need to divide by 3 on the right side of the equation:3x=24{\displaystyle 3x=24}3x3=243{\displaystyle {\frac {3x}{3}}={\frac {24}{3}}}x=8{\displaystyle x=8}
For example, if you found that x=8{\displaystyle x=8}, substitute 8 for x{\displaystyle x} in the original equation: 3(8)=24{\displaystyle 3(8)=24}. Since this equation is true, your solution is correct.
Since the variable is divided by 4, to isolate it you need to multiply by 4. x4=8{\displaystyle {\frac {x}{4}}=8} 4(x4)=(4)8{\displaystyle 4({\frac {x}{4}})=(4)8} x=32{\displaystyle x=32} Checking your work, since 324=8{\displaystyle {\frac {32}{4}}=8}, your solution is correct.
Since the constant is negative, adding it to both sides will isolate the variable. −16+x=29{\displaystyle -16+x=29} −16+x+16=29+16{\displaystyle -16+x+16=29+16} x=45{\displaystyle x=45} Checking your work, since −16+45=29{\displaystyle -16+45=29}, your solution is correct.
Since the variable is multiplied by -5, to isolate the variable, you must divide each side by -5. Remember that dividing a positive number by a negative number equals a negative quotient. −5x=45{\displaystyle -5x=45} −5x−5=45−5{\displaystyle {\frac {-5x}{-5}}={\frac {45}{-5}}} x=−9{\displaystyle x=-9} Checking your work, since −5(−9)=45{\displaystyle -5(-9)=45}, your solution is correct.
