Question

Solve and check: 1 x + 3 = x + 10 x − 2 From least to greatest, the solutions are x = and x = .

Answer 1

Answer:

x= 1/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

1x+3=x+10x−2

x+3=x+10x+−2

x+3=(x+10x)+(−2)(Combine Like Terms)

x+3=11x+−2

x+3=11x−2

Step 2: Subtract 11x from both sides.

x+3−11x=11x−2−11x

−10x+3=−2

Step 3: Subtract 3 from both sides.

−10x+3−3=−2−3

−10x=−5

Step 4: Divide both sides by -10.

−10x/−10=−5/−10x=1/2

Answer 2

Answer:

The solution for the provided equation is $x=\frac{1}{2}$

Step-by-step explanation:

Consider the provided equation,

1 x + 3 = x + 10 x - 2

The above equation can be written as:

x + 3 = x + 10 x - 2

Add the like terms.

x + 3 = x (1 + 10) - 2

x + 3 = 11 x - 2

Now, add - x on both the sides of the equation.

x + 3 - x = 11 x - 2 - x

3 = 10 x - 2

Isolate the variable by adding 2 on both sides.

3 + 2 = 10 x - 2 + 2

5 = 10 x

Now, divide both the sides by 10.

$\frac{5}{10}=\frac{10x}{10}$

$\frac{1}{2}=x$

Therefore, the value of x is $\frac{1}{2}$.

Now, substitute $x=\frac{1}{2}$ in 1 x + 3 = x + 10 x - 2.

$\frac{1}{2}+3=\frac{1}{2}+\frac{10}{2}-2$

$\frac{1+6}{2}=\frac{1+10-4}{2}$

$\frac{7}{2}=\frac{7}{2}$

Which is true.

Hence, the solution for the provided equation is $x=\frac{1}{2}$.