Question

1. résous chacune des équations

a) $x + 2x + 4,1 = 14,6$
c) $0,1a = 0,05(30 - a)$

Explanation:

Part (a)

Step1: Combine like terms

We have the equation \( x + 2x+4.1 = 14.6 \). First, combine the \( x \) terms: \( x+2x = 3x \), so the equation becomes \( 3x + 4.1=14.6 \).

Step2: Subtract 4.1 from both sides

Subtract \( 4.1 \) from each side: \( 3x+4.1 - 4.1=14.6 - 4.1 \), which simplifies to \( 3x = 10.5 \).

Step3: Divide by 3

Divide both sides by \( 3 \): \( \frac{3x}{3}=\frac{10.5}{3} \), so \( x = 3.5 \).

Step1: Expand the right side

Start with the equation \( 0.1a=0.05(30 - a) \). Expand the right - hand side using the distributive property \( c(a - b)=ca - cb \). Here, \( c = 0.05 \), \( a = 30 \) and \( b=a \), so \( 0.05\times30-0.05a=1.5 - 0.05a \). The equation becomes \( 0.1a=1.5 - 0.05a \).

Step2: Add 0.05a to both sides

Add \( 0.05a \) to each side: \( 0.1a+0.05a=1.5-0.05a + 0.05a \). Combining like terms, we get \( 0.15a=1.5 \).

Step3: Divide by 0.15

Divide both sides by \( 0.15 \): \( \frac{0.15a}{0.15}=\frac{1.5}{0.15} \), so \( a = 10 \).

Answer:

\( x = 3.5 \)

Part (c)