Question

1. Frame algebraic expressions for the following:
a. Two times a number increased by three.
b. Twice a number decreased by 7
c. Twice the sum of a number and another number, which is three more than the first
number.
d. Half a number added to 12.
e. 3 times a number subtracted from 8.

Answer 1

Dear Student,
Here is the solution of your asked query:
$$\begin{gathered} \mathrm{a})\mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{x}. \\ 2\mathrm{times}\mathrm{a}\mathrm{number}=2\mathrm{x} \\ \mathrm{So}2\mathrm{times}\mathrm{a}\mathrm{number}\mathrm{increased}\mathrm{by}3=2\mathrm{x}+3 \\ \mathrm{b})\mathrm{Twice}\mathrm{a}\mathrm{number}=2\mathrm{x} \\ \mathrm{Twice}\mathrm{a}\mathrm{number}\mathrm{decreased}\mathrm{by}7=2\mathrm{x}-7 \\ \mathrm{c})\mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{number}\mathrm{be}\mathrm{x}. \\ \mathrm{Another}\mathrm{number}\mathrm{is}3\mathrm{more}\mathrm{than}\mathrm{first}\mathrm{number} \\ \mathrm{so}\mathrm{another}\mathrm{number}=\mathrm{x}+3 \\ \mathrm{so}\mathrm{twice}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{a}\mathrm{number}\mathrm{and}\mathrm{another}\mathrm{number}=2\left(\mathrm{x}+\mathrm{x}+3\right) \\ \mathrm{d})\mathrm{Half}\mathrm{of}\mathrm{number}=\frac{\mathrm{x}}{2} \\ \mathrm{Half}\mathrm{of}\mathrm{number}\mathrm{added}\mathrm{to}12=\frac{\mathrm{x}}{2}+12 \\ \mathrm{e})3\mathrm{times}\mathrm{a}\mathrm{number}=3\mathrm{x} \\ 3\mathrm{times}\mathrm{a}\mathrm{number}\mathrm{subtracted}\mathrm{from}8=8-3\mathrm{x} \end{gathered}$$
Regards