Question

dans chaque cas:

1. résous l’équation par la méthode essais et er
2. valide ta réponse.

a) 3x + 4 = 10

b) 2x − 9 = 5

c) 7 = 4x − 5

d) 5x + 3 = 8

e) 8 = 3x + 5,6

f) 18 + 2x = 12

g) \\(\frac{x}{10} - 1,5\\) = ... (partially visible)

Explanation:

a) Equation: $3x + 4 = 10$

Step1: Isolate the $3x$ term

Subtract 4 from both sides:
$3x + 4 - 4 = 10 - 4$
$3x = 6$

Step2: Solve for $x$

Divide both sides by 3:
$\frac{3x}{3} = \frac{6}{3}$
$x = 2$

Step3: Validate the solution

Substitute $x=2$ into original equation:
$3(2) + 4 = 6 + 4 = 10$
Left side = Right side, so valid.

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b) Equation: $2x - 9 = 5$

Step1: Isolate the $2x$ term

Add 9 to both sides:
$2x - 9 + 9 = 5 + 9$
$2x = 14$

Step2: Solve for $x$

Divide both sides by 2:
$\frac{2x}{2} = \frac{14}{2}$
$x = 7$

Step3: Validate the solution

Substitute $x=7$ into original equation:
$2(7) - 9 = 14 - 9 = 5$
Left side = Right side, so valid.

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c) Equation: $7 = 4x - 5$

Step1: Isolate the $4x$ term

Add 5 to both sides:
$7 + 5 = 4x - 5 + 5$
$12 = 4x$

Step2: Solve for $x$

Divide both sides by 4:
$\frac{12}{4} = \frac{4x}{4}$
$x = 3$

Step3: Validate the solution

Substitute $x=3$ into original equation:
$7 = 4(3) - 5 = 12 - 5 = 7$
Left side = Right side, so valid.

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d) Equation: $5x + 3 = 8$

Step1: Isolate the $5x$ term

Subtract 3 from both sides:
$5x + 3 - 3 = 8 - 3$
$5x = 5$

Step2: Solve for $x$

Divide both sides by 5:
$\frac{5x}{5} = \frac{5}{5}$
$x = 1$

Step3: Validate the solution

Substitute $x=1$ into original equation:
$5(1) + 3 = 5 + 3 = 8$
Left side = Right side, so valid.

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e) Equation: $8 = 3x + 5.6$

Step1: Isolate the $3x$ term

Subtract 5.6 from both sides:
$8 - 5.6 = 3x + 5.6 - 5.6$
$2.4 = 3x$

Step2: Solve for $x$

Divide both sides by 3:
$\frac{2.4}{3} = \frac{3x}{3}$
$x = 0.8$

Step3: Validate the solution

Substitute $x=0.8$ into original equation:
$8 = 3(0.8) + 5.6 = 2.4 + 5.6 = 8$
Left side = Right side, so valid.

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f) Equation: $18 + 2x = 12$

Step1: Isolate the $2x$ term

Subtract 18 from both sides:
$18 + 2x - 18 = 12 - 18$
$2x = -6$

Step2: Solve for $x$

Divide both sides by 2:
$\frac{2x}{2} = \frac{-6}{2}$
$x = -3$

Step3: Validate the solution

Substitute $x=-3$ into original equation:
$18 + 2(-3) = 18 - 6 = 12$
Left side = Right side, so valid.

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g) Equation: $\frac{x}{10} - 1.5 = 0$ (completed from visible text)

Step1: Isolate the $\frac{x}{10}$ term

Add 1.5 to both sides:
$\frac{x}{10} - 1.5 + 1.5 = 0 + 1.5$
$\frac{x}{10} = 1.5$

Step2: Solve for $x$

Multiply both sides by 10:
$x = 1.5 \times 10$
$x = 15$

Step3: Validate the solution

Substitute $x=15$ into original equation:
$\frac{15}{10} - 1.5 = 1.5 - 1.5 = 0$
Left side = Right side, so valid.

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h) Equation: $0.75x - 12.8 = -12.65$

Step1: Isolate the $0.75x$ term

Add 12.8 to both sides:
$0.75x - 12.8 + 12.8 = -12.65 + 12.8$
$0.75x = 0.15$

Step2: Solve for $x$

Divide both sides by 0.75:
$\frac{0.75x}{0.75} = \frac{0.15}{0.75}$
$x = 0.2$

Step3: Validate the solution

Substitute $x=0.2$ into original equation:
$0.75(0.2) - 12.8 = 0.15 - 12.8 = -12.65$
Left side = Right side, so valid.

Answer:

a) $x=2$
b) $x=7$
c) $x=3$
d) $x=1$
e) $x=0.8$
f) $x=-3$
g) $x=15$
h) $x=0.2$