Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(4x+7)=-14-(3+x)\)
2. \(3(-4x-5)=-2-(-14+x)\)
3. \(5(-5x-4)=-15+(9+x)\)
4. \(4(3x+6)=-13+(-3+x)\)
5. \(5(4x-3)=-13-(-9+x)\)
6. \(5(6x+4)=5-(-7+x)\)
7. \(5(6x+1)=-15-(-15+x)\)
8. \(5(2x+1)=13+(9+3x)\)
9. \(4(-5x+7)=6-(-9+x)\)
10. \(4(3x-1)=-12+(-6+x)\)
11. \(4(2x+6)=-6+(-13+x)\)
12. \(4(-2x+3)=15-(-10+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x+7)& = & -14 \color{red}{-} (3+x) \\\Leftrightarrow & 24x+42& = &-14-3-x \\\Leftrightarrow & 24x \color{red}{+42} & = &-17 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &-17-42 \\\Leftrightarrow & 25x& = &-59 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-59}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-59}{25} & & \\ & V = \left\{ \frac{-59}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x-5)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-15& = &-2+14-x \\\Leftrightarrow & -12x \color{red}{-15} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -12x+x& = &12+15 \\\Leftrightarrow & -11x& = &27 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{27}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-27}{11} & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x-4)& = & -15 \color{red}{+} (9+x) \\\Leftrightarrow & -25x-20& = &-15+9+x \\\Leftrightarrow & -25x \color{red}{-20} & = &-6 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -25x-x& = &-6+20 \\\Leftrightarrow & -26x& = &14 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{14}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x+6)& = & -13 \color{red}{+} (-3+x) \\\Leftrightarrow & 12x+24& = &-13-3+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-16-24 \\\Leftrightarrow & 11x& = &-40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-40}{11} & & \\ & V = \left\{ \frac{-40}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x-3)& = & -13 \color{red}{-} (-9+x) \\\Leftrightarrow & 20x-15& = &-13+9-x \\\Leftrightarrow & 20x \color{red}{-15} & = &-4 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 20x+x& = &-4+15 \\\Leftrightarrow & 21x& = &11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{11}{21} & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x+4)& = & 5 \color{red}{-} (-7+x) \\\Leftrightarrow & 30x+20& = &5+7-x \\\Leftrightarrow & 30x \color{red}{+20} & = &12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &12-20 \\\Leftrightarrow & 31x& = &-8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+1)& = & -15 \color{red}{-} (-15+x) \\\Leftrightarrow & 30x+5& = &-15+15-x \\\Leftrightarrow & 30x \color{red}{+5} & = &0 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 30x+x& = &0-5 \\\Leftrightarrow & 31x& = &-5 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-5}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-5}{31} & & \\ & V = \left\{ \frac{-5}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x+1)& = & 13 \color{red}{+} (9+3x) \\\Leftrightarrow & 10x+5& = &13+9+3x \\\Leftrightarrow & 10x \color{red}{+5} & = &22 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & 10x-3x& = &22-5 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x+7)& = & 6 \color{red}{-} (-9+x) \\\Leftrightarrow & -20x+28& = &6+9-x \\\Leftrightarrow & -20x \color{red}{+28} & = &15 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -20x+x& = &15-28 \\\Leftrightarrow & -19x& = &-13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-1)& = & -12 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-4& = &-12-6+x \\\Leftrightarrow & 12x \color{red}{-4} & = &-18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &-18+4 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x+6)& = & -6 \color{red}{+} (-13+x) \\\Leftrightarrow & 8x+24& = &-6-13+x \\\Leftrightarrow & 8x \color{red}{+24} & = &-19 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 8x-x& = &-19-24 \\\Leftrightarrow & 7x& = &-43 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-43}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-43}{7} & & \\ & V = \left\{ \frac{-43}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x+3)& = & 15 \color{red}{-} (-10+x) \\\Leftrightarrow & -8x+12& = &15+10-x \\\Leftrightarrow & -8x \color{red}{+12} & = &25 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &25-12 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)