Chapter Four — Linear Equations in One Variable
The Humongous Book of Algebra Problems
59
Subtract 10 from both sides of the equation to isolate x.
The solution to the equation is x = 26. Verify the solution by substituting it into
the original equation.
Because substituting x = 26 into the equation produces a true statement
(114 = 114), x = 26 is the correct solution.
Multiplying and Dividing to Solve an Equation
Multiply/divide both sides
Note: Problems 4.9–4.10 refer to the statement “the product of three and a number is 42.”
4.9 Express the statement as an algebraic equation in terms of x.
The word “product” indicates multiplication—the product of 3 and a number x
is 3 · x, or 3x. According to the problem, that product is equal to 42: 3x = 42.
Note: Problems 4.9–4.10 refer to the statement “the product of three and a number is 42.”
4.10 Solve the equation generated in Problem 4.9 for x.
To solve an equation, you must isolate x on one side of the equal sign. In this
case, isolating x requires you to eliminate the coefficient 3; to do so, divide both
sides of the equation by 3.
Reduce the fraction to lowest terms.
3 and x
are multiplied,
so to get rid
of 3, you have
to do the
opposite of
multiplying:
dividing.
Chapter Four — Linear Equations in One Variable
The Humongous Book of Algebra Problems
60
4.11 Solve the equation 10x = 16 for x.
To isolate x on the left side of the equation, you must eliminate its coefficient.
Apply the technique described in Problem 4.10; divide both sides of the
equation by 10.
4.12 Solve the equation for x.
Eliminate the coefficient of x to isolate the variable on the left side of the
equation. To eliminate the coefficient , multiply both sides of the equation by
its reciprocal, .
4.13 Solve the equation for x.
Rewrite the fraction as the product of x and a fractional coefficient:
.
Multiply both sides of the equation by the reciprocal of to isolate x.
To reduce this
fraction, divide the
top and bottom by 2.
Multiplying
by
is the
same as dividing
by
.
If x is alone
in the top of a
fraction, you can pull
it out of the fraction
and leave a 1 in its
place.
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