## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=-4$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $2.1x+45.2=3.2-8.4x ,$ remove first the decimal numbers by multiplying both sides by a power of $10.$ Then use the properties of equality to isolate the variable. Do checking of the solution. $\bf{\text{Solution Details:}}$ Since the largest number of decimal places a term has is $1,$ multiply both sides by $10.$ This results to \begin{array}{l}\require{cancel} 2.1x+45.2=3.2-8.4x \\\\ 10(2.1x+45.2)=10(3.2-8.4x) \\\\ 21x+452=32-84x .\end{array} Using the properties of equality to isolate the variable, the equation above is equivalent to \begin{array}{l}\require{cancel} 21x+452=32-84x \\\\ 21x+84x=32-452 \\\\ 105x=-420 \\\\ x=\dfrac{420}{105} \\\\ x=-4 .\end{array} Checking: If $x=-4,$ then \begin{array}{l}\require{cancel} 2.1(-4)+45.2=3.2-8.4(-4) \\\\ -8.4+45.2=3.2+33.6 \\\\ 36.8=36.8 \text{ (TRUE) } .\end{array} Hence, the solution is $x=-4 .$