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Matemáticas 1 · Tema 3

Ecuaciones

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Ejemplo

Resuelve las siguientes ecuaciones:

3+4(2x−1)=1−2(3−5x)3+8x−4=1−6+10x8x−10x=1−6+4−3−2x=−4x=−4−2x=2\begin{aligned} 3+4(2x-1) &= 1-2(3-5x) \\ 3+8x-4 &= 1-6+10x \\ 8x-10x &= 1-6+4-3 \\ -2x &= -4 \\ x &= \frac{-4}{-2} \\ \mathbf{x} &\mathbf{= 2} \end{aligned}
2(x−3)+7=6x−5(1+2x)2x−6+7=6x−5−10x2x−6x+10x=−5+6−76x=−6x=−66x=−1\begin{aligned} 2(x-3)+7 &= 6x-5(1+2x) \\ 2x-6+7 &= 6x-5-10x \\ 2x-6x+10x &= -5+6-7 \\ 6x &= -6 \\ x &= \frac{-6}{6} \\ \mathbf{x} &\mathbf{= -1} \end{aligned}

Ejercicios

Bloque 1
6−5(3x−1)=−9+5(4x+2)6-5(3x-1)=-9+5(4x+2)
6(x+2)−3=4x−2(4−5x)6(x+2)-3=4x-2(4-5x)
−2+3(4+7x)=1−3(x−6)-2+3(4+7x)=1-3(x-6)
2(−5x+7)+9=8x−4(1+6x)2(-5x+7)+9=8x-4(1+6x)
3x−4(x−1)=5(2x+3)−103x-4(x-1)=5(2x+3)-10
−3(−2x−8)+6=7x+5(4−2x)-3(-2x-8)+6=7x+5(4-2x)

Respuestas

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Bloque 1
6−5(3x−1)=−9+5(4x+2)6−15x+5=−9+20x+10−15x−20x=−9+10−6−5−35x=−10x=−10−35x=+27\begin{aligned} 6-5(3x-1) &= -9+5(4x+2) \\ 6-15x+5 &= -9+20x+10 \\ -15x-20x &= -9+10-6-5 \\ -35x &= -10 \\ x &= \frac{-10}{-35} \\ \mathbf{x} &\mathbf{= +\tfrac{2}{7}} \end{aligned}
6(x+2)−3=4x−2(4−5x)6x+12−3=4x−8+10x6x−4x−10x=−8−12+3−8x=−17x=−17−8x=178\begin{aligned} 6(x+2)-3 &= 4x-2(4-5x) \\ 6x+12-3 &= 4x-8+10x \\ 6x-4x-10x &= -8-12+3 \\ -8x &= -17 \\ x &= \frac{-17}{-8} \\ \mathbf{x} &\mathbf{= \tfrac{17}{8}} \end{aligned}
−2+3(4+7x)=1−3(x−6)−2+12+21x=1−3x+1821x+3x=1+18+2−1224x=9x=924x=38\begin{aligned} -2+3(4+7x) &= 1-3(x-6) \\ -2+12+21x &= 1-3x+18 \\ 21x+3x &= 1+18+2-12 \\ 24x &= 9 \\ x &= \frac{9}{24} \\ \mathbf{x} &\mathbf{= \tfrac{3}{8}} \end{aligned}
2(−5x+7)+9=8x−4(1+6x)−10x+14+9=8x−4−24x−10x−8x+24x=−14−9−46x=−27x=−276x=−92\begin{aligned} 2(-5x+7)+9 &= 8x-4(1+6x) \\ -10x+14+9 &= 8x-4-24x \\ -10x-8x+24x &= -14-9-4 \\ 6x &= -27 \\ x &= \frac{-27}{6} \\ \mathbf{x} &\mathbf{= -\tfrac{9}{2}} \end{aligned}
3x−4(x−1)=5(2x+3)−103x−4x+4=10x+15−103x−4x−10x=15−10−4−11x=1x=−111\begin{aligned} 3x-4(x-1) &= 5(2x+3)-10 \\ 3x-4x+4 &= 10x+15-10 \\ 3x-4x-10x &= 15-10-4 \\ -11x &= 1 \\ \mathbf{x} &\mathbf{= -\tfrac{1}{11}} \end{aligned}
−3(−2x−8)+6=7x+5(4−2x)6x+24+6=7x+20−10x6x−7x+10x=20−24−69x=−10x=−109x=−109\begin{aligned} -3(-2x-8)+6 &= 7x+5(4-2x) \\ 6x+24+6 &= 7x+20-10x \\ 6x-7x+10x &= 20-24-6 \\ 9x &= -10 \\ x &= \frac{-10}{9} \\ \mathbf{x} &\mathbf{= -\tfrac{10}{9}} \end{aligned}

Ejercicios extra 1

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Bloque A
8−4(2x−3)=−5+3(6x+1)8-4(2x-3)=-5+3(6x+1)
5(x+3)−7=2x−4(3−2x)5(x+3)-7=2x-4(3-2x)
−4+2(5+3x)=6−5(x−2)-4+2(5+3x)=6-5(x-2)
3(−4x+5)+8=9x−2(1+7x)3(-4x+5)+8=9x-2(1+7x)
7x−3(x−2)=4(3x+1)−97x-3(x-2)=4(3x+1)-9
−2(−5x−4)+7=8x+3(6−4x)-2(-5x-4)+7=8x+3(6-4x)
Bloque B
9−2(4x−5)=−3+6(2x+3)9-2(4x-5)=-3+6(2x+3)
4(x+6)−5=7x−3(2−4x)4(x+6)-5=7x-3(2-4x)
−6+5(2+4x)=8−2(x−7)-6+5(2+4x)=8-2(x-7)
2(−3x+8)+4=5x−6(2+3x)2(-3x+8)+4=5x-6(2+3x)
8x−5(x−3)=3(4x+2)−78x-5(x-3)=3(4x+2)-7
−4(−3x−2)+9=5x+2(7−6x)-4(-3x-2)+9=5x+2(7-6x)

Ejercicios extra 2

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Bloque C
7−3(5x−2)=−4+2(3x+6)7-3(5x-2)=-4+2(3x+6)
6(x+4)−9=3x−5(1−2x)6(x+4)-9=3x-5(1-2x)
−5+4(3+2x)=9−6(x−1)-5+4(3+2x)=9-6(x-1)
5(−2x+3)+7=4x−3(5+2x)5(-2x+3)+7=4x-3(5+2x)
9x−2(x−4)=6(2x+3)−89x-2(x-4)=6(2x+3)-8
−3(−4x−5)+2=6x+4(3−5x)-3(-4x-5)+2=6x+4(3-5x)
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