Find the value of each expression by substituting [tex]x=-3[/tex].

[tex]2 x+1=2 \times(-3)+1=[/tex]

[tex]-3 x+4=[/tex]

[tex]4+5 x=[/tex]

[tex]-2 x+3+4 x=[/tex]

Substitute x = − 3 into the expression 2 x + 1 and simplify to get − 5 .
Substitute x = − 3 into the expression − 3 x + 4 and simplify to get 13 .
Substitute x = − 3 into the expression 4 + 5 x and simplify to get − 11 .
Substitute x = − 3 into the expression − 2 x + 3 + 4 x and simplify to get − 3 .
The values of the expressions are − 5 , 13 , − 11 , − 3 ​ .

Explanation

Problem Setup We are given the value x = − 3 and asked to evaluate four expressions by substituting this value into each one. We will carefully perform each substitution and simplify the resulting arithmetic expression.

Evaluating the First Expression First expression: 2 x + 1 . Substituting x = − 3 , we get: 2 × ( − 3 ) + 1 = − 6 + 1 = − 5

Evaluating the Second Expression Second expression: − 3 x + 4 . Substituting x = − 3 , we get: − 3 × ( − 3 ) + 4 = 9 + 4 = 13

Evaluating the Third Expression Third expression: 4 + 5 x . Substituting x = − 3 , we get: 4 + 5 × ( − 3 ) = 4 − 15 = − 11

Evaluating the Fourth Expression Fourth expression: − 2 x + 3 + 4 x . Substituting x = − 3 , we get: − 2 × ( − 3 ) + 3 + 4 × ( − 3 ) = 6 + 3 − 12 = 9 − 12 = − 3

Final Answer Therefore, the values of the expressions are − 5 , 13 , − 11 , and − 3 , respectively.


Examples
Substitution is a fundamental concept in algebra and is used extensively in various real-world applications. For example, if you are calculating the total cost of buying 'x' number of items, each costing $2, plus a fixed shipping fee of $1, the total cost can be represented as 2 x + 1 . If you buy 3 items ( x = 3 ), you substitute x with 3 to find the total cost: $2(3) + 1 = $7. Similarly, in physics, you might substitute values into equations to calculate velocity, acceleration, or force. Understanding substitution helps in making informed decisions and predictions based on mathematical models.

Answered by GinnyAnswer | 2025-07-08

The evaluated values of the expressions after substituting x = − 3 are − 5 , 13 , − 11 , and − 3 .
;

Answered by Anonymous | 2025-08-06