Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x-1)& = & 2 \color{red}{+} (13+x) \\\Leftrightarrow & -12x-3& = &2+13+x \\\Leftrightarrow & -12x \color{red}{-3} & = &15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &15+3 \\\Leftrightarrow & -13x& = &18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x+1)& = & 6 \color{red}{-} (8+x) \\\Leftrightarrow & -30x+6& = &6-8-x \\\Leftrightarrow & -30x \color{red}{+6} & = &-2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -30x+x& = &-2-6 \\\Leftrightarrow & -29x& = &-8 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-8}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{8}{29} & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x+1)& = & -9 \color{red}{-} (-15+x) \\\Leftrightarrow & 20x+5& = &-9+15-x \\\Leftrightarrow & 20x \color{red}{+5} & = &6 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 20x+x& = &6-5 \\\Leftrightarrow & 21x& = &1 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{1}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x-6)& = & -6 \color{red}{+} (-5+x) \\\Leftrightarrow & -9x-18& = &-6-5+x \\\Leftrightarrow & -9x \color{red}{-18} & = &-11 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -9x-x& = &-11+18 \\\Leftrightarrow & -10x& = &7 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{7}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-7}{10} & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+7)& = & -12 \color{red}{+} (-12-4x) \\\Leftrightarrow & -9x+21& = &-12-12-4x \\\Leftrightarrow & -9x \color{red}{+21} & = &-24 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-24 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -9x+4x& = &-24-21 \\\Leftrightarrow & -5x& = &-45 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-45}{ \color{red}{-5} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x+3)& = & -13 \color{red}{-} (14-4x) \\\Leftrightarrow & -9x+9& = &-13-14+4x \\\Leftrightarrow & -9x \color{red}{+9} & = &-27 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &-27 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & -9x-4x& = &-27-9 \\\Leftrightarrow & -13x& = &-36 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-36}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{36}{13} & & \\ & V = \left\{ \frac{36}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x+1)& = & -15 \color{red}{-} (-15-5x) \\\Leftrightarrow & -18x+6& = &-15+15+5x \\\Leftrightarrow & -18x \color{red}{+6} & = &0 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -18x-5x& = &0-6 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-3)& = & 15 \color{red}{+} (14-5x) \\\Leftrightarrow & -8x-6& = &15+14-5x \\\Leftrightarrow & -8x \color{red}{-6} & = &29 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &29 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -8x+5x& = &29+6 \\\Leftrightarrow & -3x& = &35 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{35}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-35}{3} & & \\ & V = \left\{ \frac{-35}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+4)& = & 3 \color{red}{-} (-1+x) \\\Leftrightarrow & 24x+24& = &3+1-x \\\Leftrightarrow & 24x \color{red}{+24} & = &4 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &4-24 \\\Leftrightarrow & 25x& = &-20 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-20}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-6)& = & 10 \color{red}{+} (1-5x) \\\Leftrightarrow & -18x-36& = &10+1-5x \\\Leftrightarrow & -18x \color{red}{-36} & = &11 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -18x+5x& = &11+36 \\\Leftrightarrow & -13x& = &47 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{47}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-47}{13} & & \\ & V = \left\{ \frac{-47}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x+6)& = & 14 \color{red}{-} (7+x) \\\Leftrightarrow & -15x+30& = &14-7-x \\\Leftrightarrow & -15x \color{red}{+30} & = &7 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -15x+x& = &7-30 \\\Leftrightarrow & -14x& = &-23 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-23}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{23}{14} & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x-4)& = & -12 \color{red}{+} (-5+x) \\\Leftrightarrow & 9x-12& = &-12-5+x \\\Leftrightarrow & 9x \color{red}{-12} & = &-17 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 9x-x& = &-17+12 \\\Leftrightarrow & 8x& = &-5 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-5}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-5}{8} & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)