Question

1. if ( x + 3 = 4 ), find the value of ( x^2 - 19 ).
2. solve for ( y ): ( 6y + x - 4y - 6 + 5x = 0 )
3. find the least common multiple (lcm) of 8, 36, and 75.

Explanation:

Step1: Solve for x from given equation

$x + 3 = 4 \implies x = 4 - 3 = 1$

Step2: Substitute x into expression

$x^2 - 19 = 1^2 - 19$

Step3: Calculate final value

$1 - 19 = -18$

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Step1: Combine like terms for y

$6y + x - 4y - 6 + 5x = 0 \implies (6y - 4y) + (x + 5x) - 6 = 0$

Step2: Simplify the equation

$2y + 6x - 6 = 0$

Step3: Isolate terms with y

$2y = 6 - 6x$

Step4: Solve for y

$y = \frac{6 - 6x}{2} = 3 - 3x$

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Step1: Prime factorize each number

$8 = 2^3$, $36 = 2^2 \times 3^2$, $75 = 3 \times 5^2$

Step2: Take highest power of each prime

$\text{LCM} = 2^3 \times 3^2 \times 5^2$

Step3: Compute the product

$8 \times 9 \times 25 = 1800$

Answer:

1. $\boldsymbol{-18}$
2. $\boldsymbol{y = 3 - 3x}$
3. $\boldsymbol{1800}$