Math / Algebra

QuestionQuestions à choix multiples (1) Quel point appartient à l'ensemble-solution de l'inéquation $2 x+5 y<24$ ? a) $A(7,2)$ b) $\mathrm{B}(2,7)$ (c)) $\mathrm{C}(-3,5)$ d) $D(5,3)$

Studdy Solution

STEP 1

1. We are given the inequality $2x + 5y < 24$ .
2. We need to determine which point among the given options satisfies the inequality.

STEP 2

1. Substitute each point into the inequality.
2. Check if the inequality holds true for each point.
3. Identify the point(s) that satisfy the inequality.

STEP 3

Substitute point $A(7,2)$ into the inequality $2x + 5y < 24$ .
$2(7) + 5(2) = 14 + 10 = 24$

STEP 4

Check if the inequality holds for point $A(7,2)$ .
Since $24 \not< 24$ , point $A(7,2)$ does not satisfy the inequality.

STEP 5

Substitute point $B(2,7)$ into the inequality $2x + 5y < 24$ .
$2(2) + 5(7) = 4 + 35 = 39$

STEP 6

Check if the inequality holds for point $B(2,7)$ .
Since $39 \not< 24$ , point $B(2,7)$ does not satisfy the inequality.

STEP 7

Substitute point $C(-3,5)$ into the inequality $2x + 5y < 24$ .
$2(-3) + 5(5) = -6 + 25 = 19$

STEP 8

Check if the inequality holds for point $C(-3,5)$ .
Since $19 < 24$ , point $C(-3,5)$ satisfies the inequality.

STEP 9

Substitute point $D(5,3)$ into the inequality $2x + 5y < 24$ .
$2(5) + 5(3) = 10 + 15 = 25$

STEP 10

Check if the inequality holds for point $D(5,3)$ .
Since $25 \not< 24$ , point $D(5,3)$ does not satisfy the inequality.
The point that satisfies the inequality is:
$\boxed{C(-3,5)}$

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QuestionQuestions à choix multiples (1) Quel point appartient à l'ensemble-solution de l'inéquation $2 x+5 y<24$ ? a) $A(7,2)$ b) $\mathrm{B}(2,7)$ (c)) $\mathrm{C}(-3,5)$ d) $D(5,3)$

Studdy Solution

STEP 1

1. We are given the inequality $2x + 5y < 24$ .
2. We need to determine which point among the given options satisfies the inequality.

STEP 2

1. Substitute each point into the inequality.
2. Check if the inequality holds true for each point.
3. Identify the point(s) that satisfy the inequality.

STEP 3

Substitute point $A(7,2)$ into the inequality $2x + 5y < 24$ .
$2(7) + 5(2) = 14 + 10 = 24$

STEP 4

Check if the inequality holds for point $A(7,2)$ .
Since $24 \not< 24$ , point $A(7,2)$ does not satisfy the inequality.

STEP 5

Substitute point $B(2,7)$ into the inequality $2x + 5y < 24$ .
$2(2) + 5(7) = 4 + 35 = 39$

STEP 6

Check if the inequality holds for point $B(2,7)$ .
Since $39 \not< 24$ , point $B(2,7)$ does not satisfy the inequality.

STEP 7

Substitute point $C(-3,5)$ into the inequality $2x + 5y < 24$ .
$2(-3) + 5(5) = -6 + 25 = 19$

STEP 8

Check if the inequality holds for point $C(-3,5)$ .
Since $19 < 24$ , point $C(-3,5)$ satisfies the inequality.

STEP 9

Substitute point $D(5,3)$ into the inequality $2x + 5y < 24$ .
$2(5) + 5(3) = 10 + 15 = 25$

STEP 10

Check if the inequality holds for point $D(5,3)$ .
Since $25 \not< 24$ , point $D(5,3)$ does not satisfy the inequality.
The point that satisfies the inequality is:
$\boxed{C(-3,5)}$

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QuestionQuestions à choix multiples (1) Quel point appartient à l'ensemble-solution de l'inéquation 2x+5y<242 x+5 y<242x+5y<24 ? a) A(7,2)A(7,2)A(7,2) b) B(2,7)\mathrm{B}(2,7)B(2,7) (c)) C(−3,5)\mathrm{C}(-3,5)C(−3,5) d) D(5,3)D(5,3)D(5,3)

Studdy Solution

STEP 1

1. We are given the inequality 2x+5y<242x + 5y < 242x+5y<24.2. We need to determine which point among the given options satisfies the inequality.

STEP 2

1. Substitute each point into the inequality.2. Check if the inequality holds true for each point.3. Identify the point(s) that satisfy the inequality.

STEP 3

Substitute point A(7,2)A(7,2)A(7,2) into the inequality 2x+5y<242x + 5y < 242x+5y<24.2(7)+5(2)=14+10=24 2(7) + 5(2) = 14 + 10 = 24 2(7)+5(2)=14+10=24

STEP 4

Check if the inequality holds for point A(7,2)A(7,2)A(7,2).Since 24≮2424 \not< 2424<24, point A(7,2)A(7,2)A(7,2) does not satisfy the inequality.

STEP 5

Substitute point B(2,7)B(2,7)B(2,7) into the inequality 2x+5y<242x + 5y < 242x+5y<24.2(2)+5(7)=4+35=39 2(2) + 5(7) = 4 + 35 = 39 2(2)+5(7)=4+35=39

STEP 6

Check if the inequality holds for point B(2,7)B(2,7)B(2,7).Since 39≮2439 \not< 2439<24, point B(2,7)B(2,7)B(2,7) does not satisfy the inequality.

STEP 7

Substitute point C(−3,5)C(-3,5)C(−3,5) into the inequality 2x+5y<242x + 5y < 242x+5y<24.2(−3)+5(5)=−6+25=19 2(-3) + 5(5) = -6 + 25 = 19 2(−3)+5(5)=−6+25=19

STEP 8

Check if the inequality holds for point C(−3,5)C(-3,5)C(−3,5).Since 19<2419 < 2419<24, point C(−3,5)C(-3,5)C(−3,5) satisfies the inequality.

STEP 9

Substitute point D(5,3)D(5,3)D(5,3) into the inequality 2x+5y<242x + 5y < 242x+5y<24.2(5)+5(3)=10+15=25 2(5) + 5(3) = 10 + 15 = 25 2(5)+5(3)=10+15=25

STEP 10

Check if the inequality holds for point D(5,3)D(5,3)D(5,3).Since 25≮2425 \not< 2425<24, point D(5,3)D(5,3)D(5,3) does not satisfy the inequality. The point that satisfies the inequality is:C(−3,5) \boxed{C(-3,5)} C(−3,5)​

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QuestionQuestions à choix multiples (1) Quel point appartient à l'ensemble-solution de l'inéquation $2 x+5 y<24$ ? a) $A(7,2)$ b) $\mathrm{B}(2,7)$ (c)) $\mathrm{C}(-3,5)$ d) $D(5,3)$

1. We are given the inequality $2x + 5y < 24$ .
2. We need to determine which point among the given options satisfies the inequality.

1. Substitute each point into the inequality.
2. Check if the inequality holds true for each point.
3. Identify the point(s) that satisfy the inequality.

Substitute point $A(7,2)$ into the inequality $2x + 5y < 24$ .
$2(7) + 5(2) = 14 + 10 = 24$

Check if the inequality holds for point $A(7,2)$ .
Since $24 \not< 24$ , point $A(7,2)$ does not satisfy the inequality.

Substitute point $B(2,7)$ into the inequality $2x + 5y < 24$ .
$2(2) + 5(7) = 4 + 35 = 39$

Check if the inequality holds for point $B(2,7)$ .
Since $39 \not< 24$ , point $B(2,7)$ does not satisfy the inequality.

Substitute point $C(-3,5)$ into the inequality $2x + 5y < 24$ .
$2(-3) + 5(5) = -6 + 25 = 19$

Check if the inequality holds for point $C(-3,5)$ .
Since $19 < 24$ , point $C(-3,5)$ satisfies the inequality.

Substitute point $D(5,3)$ into the inequality $2x + 5y < 24$ .
$2(5) + 5(3) = 10 + 15 = 25$

Check if the inequality holds for point $D(5,3)$ .
Since $25 \not< 24$ , point $D(5,3)$ does not satisfy the inequality.
The point that satisfies the inequality is:
$\boxed{C(-3,5)}$