Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-5)& = & -7 \color{red}{-} (15+x) \\\Leftrightarrow & 2x-10& = &-7-15-x \\\Leftrightarrow & 2x \color{red}{-10} & = &-22 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &-22+10 \\\Leftrightarrow & 3x& = &-12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-12}{ \color{red}{3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x+2)& = & 12 \color{red}{+} (-7+x) \\\Leftrightarrow & -20x+10& = &12-7+x \\\Leftrightarrow & -20x \color{red}{+10} & = &5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -20x-x& = &5-10 \\\Leftrightarrow & -21x& = &-5 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-5}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{5}{21} & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (6x-3)& = & -3 \color{red}{-} (-14+x) \\\Leftrightarrow & 24x-12& = &-3+14-x \\\Leftrightarrow & 24x \color{red}{-12} & = &11 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &11+12 \\\Leftrightarrow & 25x& = &23 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{23}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{23}{25} & & \\ & V = \left\{ \frac{23}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+5)& = & 4 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x+20& = &4-15+x \\\Leftrightarrow & -20x \color{red}{+20} & = &-11 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &-11-20 \\\Leftrightarrow & -21x& = &-31 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-31}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{31}{21} & & \\ & V = \left\{ \frac{31}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+4)& = & 9 \color{red}{-} (-9+x) \\\Leftrightarrow & 15x+12& = &9+9-x \\\Leftrightarrow & 15x \color{red}{+12} & = &18 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 15x+x& = &18-12 \\\Leftrightarrow & 16x& = &6 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{6}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-4)& = & -14 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-16& = &-14+6+x \\\Leftrightarrow & -12x \color{red}{-16} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -12x-x& = &-8+16 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x-2)& = & 10 \color{red}{-} (-11+x) \\\Leftrightarrow & -36x-12& = &10+11-x \\\Leftrightarrow & -36x \color{red}{-12} & = &21 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -36x+x& = &21+12 \\\Leftrightarrow & -35x& = &33 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{33}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-33}{35} & & \\ & V = \left\{ \frac{-33}{35} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-6)& = & 7 \color{red}{+} (13-5x) \\\Leftrightarrow & -6x-36& = &7+13-5x \\\Leftrightarrow & -6x \color{red}{-36} & = &20 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -6x+5x& = &20+36 \\\Leftrightarrow & -x& = &56 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{56}{ \color{red}{-1} } \\\Leftrightarrow & x = -56 & & \\ & V = \left\{ -56 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-2)& = & 11 \color{red}{+} (10+x) \\\Leftrightarrow & 12x-12& = &11+10+x \\\Leftrightarrow & 12x \color{red}{-12} & = &21 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &21+12 \\\Leftrightarrow & 11x& = &33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{33}{ \color{red}{11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x+4)& = & -15 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x+24& = &-15+4-x \\\Leftrightarrow & 12x \color{red}{+24} & = &-11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &-11-24 \\\Leftrightarrow & 13x& = &-35 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-35}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-35}{13} & & \\ & V = \left\{ \frac{-35}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+3)& = & -14 \color{red}{-} (-6+x) \\\Leftrightarrow & -30x+15& = &-14+6-x \\\Leftrightarrow & -30x \color{red}{+15} & = &-8 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &-8-15 \\\Leftrightarrow & -29x& = &-23 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-23}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{23}{29} & & \\ & V = \left\{ \frac{23}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x-4)& = & 1 \color{red}{+} (5+x) \\\Leftrightarrow & -18x-24& = &1+5+x \\\Leftrightarrow & -18x \color{red}{-24} & = &6 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -18x-x& = &6+24 \\\Leftrightarrow & -19x& = &30 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{30}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-30}{19} & & \\ & V = \left\{ \frac{-30}{19} \right\} & \\\end{align}\)