Introduction to linear functions and inequalities:<\p>

Linear Functions:<\p>

In mathematics, the compass linear function encyst refer into either anent two different but related concepts:<\p>

a first-degree polynomial function of one variable;<\p>

a map between couplet vector spaces that preserves vector happenstance and scalar fructification.<\p>

Inequalities<\p>

Inflowing mathematics, an inequality is a statement in connection with the relative size octofoil brotherhood of two objects or about whether they are the same or not<\p>

The notation a

The opera score a > b pool that a is greater than b.<\p>

The single entry a? b contrivance that a is not opposite number unto b, but does not say that one is eclipsing by comparison with the other spread eagle even that they can be compared in span. (source: wikipedia)<\p>

Linear Functions Problems:<\p>

linear functions 1:<\p>

Decide the expression<\p>

5(-3y - 2) - (y - 3) = - 4(4y + 5) + 13<\p>

Solution:<\p>

€ Disposed to the equation<\p>

5(-3y - 2) - (y - 3) = -4(4y + 5) + 13<\p>

€ Multiply factors.<\p>

-15y - 10 - y + 3 = -16y - 20 +13<\p>

€ Group like terms.<\p>

-16y - 7 = -16y - 7<\p>

€ Add 16y + 7 to both sides and whomp up the expression identically follows<\p>

0 = 0<\p>

€ The above statement is true vice all values of y and therefore all real numbers are solutions on the escape clause equation.<\p>

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Problem seeing that algebra 1 linear functions 2:<\p>

Solve the sequent equation for x in the consimilar equation.<\p>

2x - 4 = 10<\p>

Solution:<\p>

€ Given equation<\p>

2x - 4 = 10<\p>

€Add 4 unto both sides in regard to the equation:<\p>

2x = 14<\p>

€ Divide set of two sides by 2:<\p>

X = 7<\p>

€The dispatch is x = 7.<\p>

Check the solution in agreement with substituting 7 up-to-date the original equation for mark of signature. If the surplus side of the expression equals the perfectly team up with of the factor after the substitution, you hear of settle the correct answe Inequalities Problem:<\p>

Inequalities problem solver- Example 1:<\p>

Solve 4x + 3

Countermove:<\p>

4x + 3

4x +3 - 3

4x

4x - 8x

- 4x

x > - 1<\p>

The solution set is }0, 1, 2, 3€ }<\p>

inequalities little problem solver - Example 2:<\p>

Solve 6y - 8

(her) €y' is an integer,<\p>

(ii) €y' is a whole persuasion.<\p>

Solution:<\p>

Presumed, 6y - 8

6y - 8 + 8

6y

6y - 2y

4y

y

(unit)When €y' is an integer, furthermore the solutions are<\p>

..., - 3, - 2, - 1, 0, 1, 2<\p>

(ii) Yet €y' is a whole number, extra<\p>