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Classify the equation as a conditional equation., an jdentity, or a contradiction and then state the solution.
8(1-3x)+15(2x+7)=2(x+50)+4(x+3)+1

Respuesta :

msm555

Answer:

Classification: identity equation

Solution: all real numbers

Step-by-step explanation:

To solve the equation [tex]8(1-3x)+15(2x+7)=2(x+50)+4(x+3)+1[/tex], let's simplify it:

Expand both sides:

[tex] 8 - 24x + 30x + 105 = 2x + 100 + 4x + 12 + 1 [/tex]

Combine like terms:

[tex] 8 + 6x + 105 = 6x + 113 [/tex]

[tex] 6x + 113 = 6x + 113 [/tex]

Subtract [tex]6x + 113[/tex] from both sides:

[tex] 0 = 0 [/tex]

The equation [tex]0 = 0[/tex] is an identity because it is always true, regardless of the value of [tex]x[/tex].

Therefore, the solution to the equation is all real numbers [tex]x[/tex]. Since the equation simplifies the same expression on both sides, it is an identity.

semsee45

Answer:

Identity equation

Step-by-step explanation:

Classifications of equations

  • A conditional equation is an equation that holds true only for certain values of x.
  • An identity is an equation that is true for all values of x.
  • A contradiction is an equation that is never true, regardless of the values of x.

To determine the classification of the given equation, we can simplify the left and right sides, and solve for x:

[tex]\begin{aligned}8(1-3x)+15(2x+7)&=2(x+50)+4(x+3)+1\\\\8-24x+30x+105&=2x+100+4x+12+1\\\\30x-24x+105+8&=4x+2x+100+12+1\\\\6x+113&=6x+113\\\\6x+113-113&=6x+113-113\\\\6x&=6x\\\\\dfrac{6x}{6}&=\dfrac{6x}{6}\\\\x&=x\end{aligned}[/tex]

Therefore, we have shown that both sides of the equation simplify to the same expression, x. This implies that, regardless of the value we substitute for x, both sides will always be equal. Consequently, the equation is an identity.

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