Question

write the following as an equation. then solve. twice the difference of a number and 4 is equal to three times the sum of the number and 5. find the number. (type an equation using x as the variable. use integers or fractions for any numbers in the equation. do not simplify.) the equation is □

Explanation:

Step1: Translate the sentence into an equation

Let the number be \(x\). The difference of a number and 4 is \(x - 4\), twice this difference is \(2(x - 4)\). The sum of the number and 5 is \(x+5\), three - times this sum is \(3(x + 5)\). The equation is \(2(x - 4)=3(x + 5)\).

Step2: Expand both sides of the equation

Using the distributive property \(a(b + c)=ab+ac\), we get \(2x-8 = 3x+15\).

Step3: Isolate the variable \(x\)

Subtract \(2x\) from both sides: \(-8=x + 15\). Then subtract 15 from both sides: \(x=-8 - 15\).

Step4: Calculate the value of \(x\)

\(x=-23\).

Answer:

The equation is \(2(x - 4)=3(x + 5)\) and the number \(x=-23\)