a/3 + 1 = 3, solve for a. 8) 4x, 8xy, 6xyz, find the LCM. 7) Find the LCM of the given numbers. 6) Simplify…

Question

a/3 + 1 = 3, solve for a. 8) 4x, 8xy, 6xyz, find the LCM. 7) Find the LCM of the given numbers. 6) Simplify the expression 5(y−2)−2y

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

:

Distribute the 5 into the parenthesis.
$5(y-2) - 2y = 5y - 5 \times 2 - 2y$ $5y - 10 - 2y$
Combine the like terms ( $5y$ and $-2y$ ).
$(5y - 2y) - 10 = 3y - 10$
The final answer is $\boxed{3y - 10}$ .

:
Identify the integers marked on the number line.
The number line shows integers from -5 to 4.
The integers are $\boxed{\text{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4}}$ .

:
Find the Least Common Multiple (LCM) of the numerical coefficients
4, 8, and 6.
Prime factorization:
$4 = 2^2$
$8 = 2^3$
$6 = 2 \times 3$
The LCM of (4, 8, 6) is $2^3 \times 3 = 8 \times 3 = 24$ .
Find the LCM of the variable parts
$x$ , $xy$ , and $xyz$ .
The highest power of $x$ is $x^1$ .
The highest power of $y$ is $y^1$ .
The highest power of $z$ is $z^1$ .
The LCM of the variables is $xyz$ .
Combine the numerical LCM and the variable LCM.
The LCM of $4x$ , $8xy$ , and $6xyz$ is $24xyz$ .
The final answer is $\boxed{24xyz}$ .

:
Subtract 1 from both sides of the equation.
$\frac{a}{3} + 1 = 3$ $\frac{a}{3} = 3 - 1$ $\frac{a}{3} = 2$
Multiply both sides by 3 to solve for $a$ .
$a = 2 \times 3$ $a = 6$
The final answer is $\boxed{6}$ .

A/3 + 1 = 3, solve for a. 8) 4x, 8xy, 6xyz, find the LCM. 7) Find the LCM of the given numbers. 6) Simplify the expression 5(y-2)-2y