Question

classwork
mr. diaz
math concepts
hw 39
solve for x:
(1) $5x - 4 = 4.6$
(2) solve $\frac{2}{3}x - 25 = 7$

1. the lengths of the sides of a triangle are represented by $8x$, $7x$, and $5x$. express the perimeter of the triangle in terms of $x$.

las longitudes de los lados de un triángulo se representan mediante $8x$, $7x$ y $5x$. expresa el perímetro del triángulo en términos de $x$.
longè kote yon triyang yo reprezante pa $8x$, $7x$, ak $5x$. eksprime perimèt la nan triyang lan an tèm de $x$.

1. from $4a^2 - 9a + 2$ subtract $3a^2 - 9a + 8$

Explanation:

Question 1: Solve for \( x \) in \( 5x - 4 = 4.6 \)

Step 1: Add 4 to both sides

To isolate the term with \( x \), we add 4 to both sides of the equation.
\( 5x - 4 + 4 = 4.6 + 4 \)
Simplifying both sides, we get:
\( 5x = 8.6 \)

Step 2: Divide by 5

To solve for \( x \), we divide both sides by 5.
\( x = \frac{8.6}{5} \)
Calculating the right-hand side, we find:
\( x = 1.72 \)

Step 1: Add 25 to both sides

To isolate the term with \( x \), we add 25 to both sides of the equation.
\( \frac{2}{3}x - 25 + 25 = 7 + 25 \)
Simplifying both sides, we get:
\( \frac{2}{3}x = 32 \)

Step 2: Multiply by \( \frac{3}{2} \)

To solve for \( x \), we multiply both sides by \( \frac{3}{2} \).
\( x = 32 \times \frac{3}{2} \)
Calculating the right-hand side, we find:
\( x = 48 \)

The perimeter of a triangle is the sum of the lengths of its three sides. The sides are \( 8x \), \( 7x \), and \( 5x \).

Step 1: Sum the sides

Perimeter \( P = 8x + 7x + 5x \)

Step 2: Combine like terms

Combining the like terms (terms with \( x \)):
\( P = (8 + 7 + 5)x \)
\( P = 20x \)

Answer:

\( x = 1.72 \)

Question 2: Solve \( \frac{2}{3}x - 25 = 7 \)