Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x-6)& = & -9 \color{red}{-} (-14+x) \\\Leftrightarrow & 20x-24& = &-9+14-x \\\Leftrightarrow & 20x \color{red}{-24} & = &5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &5+24 \\\Leftrightarrow & 21x& = &29 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{29}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{29}{21} & & \\ & V = \left\{ \frac{29}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-2)& = & 10 \color{red}{+} (-8+x) \\\Leftrightarrow & -15x-10& = &10-8+x \\\Leftrightarrow & -15x \color{red}{-10} & = &2 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -15x-x& = &2+10 \\\Leftrightarrow & -16x& = &12 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{12}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-3}{4} & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x-2)& = & -4 \color{red}{+} (12+x) \\\Leftrightarrow & 12x-8& = &-4+12+x \\\Leftrightarrow & 12x \color{red}{-8} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &8+8 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-2)& = & -12 \color{red}{-} (7+x) \\\Leftrightarrow & 24x-12& = &-12-7-x \\\Leftrightarrow & 24x \color{red}{-12} & = &-19 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &-19+12 \\\Leftrightarrow & 25x& = &-7 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-7}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-7}{25} & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x-2)& = & -4 \color{red}{+} (1+4x) \\\Leftrightarrow & 9x-6& = &-4+1+4x \\\Leftrightarrow & 9x \color{red}{-6} & = &-3 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & 9x-4x& = &-3+6 \\\Leftrightarrow & 5x& = &3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-6)& = & 6 \color{red}{-} (15-5x) \\\Leftrightarrow & 18x-18& = &6-15+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &-9+18 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-4)& = & 15 \color{red}{-} (-7+x) \\\Leftrightarrow & -9x-12& = &15+7-x \\\Leftrightarrow & -9x \color{red}{-12} & = &22 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -9x+x& = &22+12 \\\Leftrightarrow & -8x& = &34 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{34}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-17}{4} & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x-7)& = & -1 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x-42& = &-1+12-x \\\Leftrightarrow & -24x \color{red}{-42} & = &11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &11+42 \\\Leftrightarrow & -23x& = &53 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{53}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-53}{23} & & \\ & V = \left\{ \frac{-53}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+6)& = & 4 \color{red}{+} (5+x) \\\Leftrightarrow & -36x+36& = &4+5+x \\\Leftrightarrow & -36x \color{red}{+36} & = &9 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -36x-x& = &9-36 \\\Leftrightarrow & -37x& = &-27 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-27}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{27}{37} & & \\ & V = \left\{ \frac{27}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x-1)& = & -10 \color{red}{+} (-11-3x) \\\Leftrightarrow & 10x-2& = &-10-11-3x \\\Leftrightarrow & 10x \color{red}{-2} & = &-21 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 10x+3x& = &-21+2 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x-3)& = & 2 \color{red}{-} (-14+x) \\\Leftrightarrow & -2x-6& = &2+14-x \\\Leftrightarrow & -2x \color{red}{-6} & = &16 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -2x+x& = &16+6 \\\Leftrightarrow & -x& = &22 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{22}{ \color{red}{-1} } \\\Leftrightarrow & x = -22 & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x+5)& = & -3 \color{red}{-} (1+3x) \\\Leftrightarrow & 2x+10& = &-3-1-3x \\\Leftrightarrow & 2x \color{red}{+10} & = &-4 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 2x+3x& = &-4-10 \\\Leftrightarrow & 5x& = &-14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)