Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x-4)& = & -8 \color{red}{-} (10+x) \\\Leftrightarrow & 12x-8& = &-8-10-x \\\Leftrightarrow & 12x \color{red}{-8} & = &-18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &-18+8 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+5)& = & 8 \color{red}{-} (-15+3x) \\\Leftrightarrow & 20x+20& = &8+15-3x \\\Leftrightarrow & 20x \color{red}{+20} & = &23 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 20x+3x& = &23-20 \\\Leftrightarrow & 23x& = &3 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{3}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-4)& = & -9 \color{red}{-} (-9+x) \\\Leftrightarrow & 4x-8& = &-9+9-x \\\Leftrightarrow & 4x \color{red}{-8} & = &0 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 4x+x& = &0+8 \\\Leftrightarrow & 5x& = &8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-1)& = & -3 \color{red}{-} (10+x) \\\Leftrightarrow & 12x-6& = &-3-10-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-13+6 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-7)& = & 7 \color{red}{+} (6+x) \\\Leftrightarrow & 18x-21& = &7+6+x \\\Leftrightarrow & 18x \color{red}{-21} & = &13 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 18x-x& = &13+21 \\\Leftrightarrow & 17x& = &34 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{34}{ \color{red}{17} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x+6)& = & 10 \color{red}{+} (6+x) \\\Leftrightarrow & -30x+36& = &10+6+x \\\Leftrightarrow & -30x \color{red}{+36} & = &16 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -30x-x& = &16-36 \\\Leftrightarrow & -31x& = &-20 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-20}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{20}{31} & & \\ & V = \left\{ \frac{20}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-7)& = & -7 \color{red}{+} (-7-5x) \\\Leftrightarrow & -8x-14& = &-7-7-5x \\\Leftrightarrow & -8x \color{red}{-14} & = &-14 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+14} \\\Leftrightarrow & -8x+5x& = &-14+14 \\\Leftrightarrow & -3x& = &0 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{0}{ \color{red}{-3} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x+4)& = & 4 \color{red}{+} (3-4x) \\\Leftrightarrow & 9x+12& = &4+3-4x \\\Leftrightarrow & 9x \color{red}{+12} & = &7 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & 9x+4x& = &7-12 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x+7)& = & 9 \color{red}{+} (-11-4x) \\\Leftrightarrow & 5x+35& = &9-11-4x \\\Leftrightarrow & 5x \color{red}{+35} & = &-2 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & 5x+4x& = &-2-35 \\\Leftrightarrow & 9x& = &-37 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-37}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-37}{9} & & \\ & V = \left\{ \frac{-37}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+1)& = & 11 \color{red}{-} (5-5x) \\\Leftrightarrow & -36x+6& = &11-5+5x \\\Leftrightarrow & -36x \color{red}{+6} & = &6 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -36x-5x& = &6-6 \\\Leftrightarrow & -41x& = &0 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{0}{ \color{red}{-41} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x+4)& = & -2 \color{red}{-} (-5+x) \\\Leftrightarrow & 18x+24& = &-2+5-x \\\Leftrightarrow & 18x \color{red}{+24} & = &3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 18x+x& = &3-24 \\\Leftrightarrow & 19x& = &-21 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-21}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-21}{19} & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x-5)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & -6x-15& = &8-14+x \\\Leftrightarrow & -6x \color{red}{-15} & = &-6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &-6+15 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)