Question

step 4: identify the type of number that must be chosen based on the rule.
a(n) rational (irrational) number must be chosen based on the rule. (1
point)
step 5: identify the required number from among the choices and give a reason for
your answer.
__ will produce an irrational answer when added to \\( \frac { 7 } { 8 } \\), because __ (2
points)
the sum of a rational and
irrational number is
irrational

1. use the properties of operations to simplify this algebraic expression. rewrite the

expression by following the directions in each step.
\\( 5 ( x - 4 ) + 3 x - 9 x + 7 \\)
step 1: rewrite the subtraction operations as addition of negative numbers. (1 point)
step 2: use the distributive property. (1 point)
step 3: use the commutative property of addition to reorder terms so that like terms
are together. (1 point)
1.4.4 test (tst): foundations of algebra
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Explanation:

Step1: Rewrite subtraction as addition

According to the rule \(a - b=a+( - b)\), the expression \(5(x - 4)+3x-9x + 7\) can be rewritten as \(5(x+( - 4))+3x+( - 9x)+7\).

Step2: Use the distributive property

The distributive property \(a(b + c)=ab+ac\). For \(5(x+( - 4))\), we have \(5\times x+5\times(-4)=5x-20\). So the expression becomes \(5x-20 + 3x+( - 9x)+7\).

Step3: Use the commutative property of addition

The commutative property of addition \(a + b=b + a\). Rearranging the terms, we get \(5x+3x+( - 9x)-20 + 7\).

Answer:

Step1: \(5(x+( - 4))+3x+( - 9x)+7\)
Step2: \(5x-20 + 3x+( - 9x)+7\)
Step3: \(5x+3x+( - 9x)-20 + 7\)