Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x+2)& = & 7 \color{red}{-} (-8+x) \\\Leftrightarrow & 24x+12& = &7+8-x \\\Leftrightarrow & 24x \color{red}{+12} & = &15 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 24x+x& = &15-12 \\\Leftrightarrow & 25x& = &3 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{3}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{3}{25} & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+3)& = & 12 \color{red}{+} (13+x) \\\Leftrightarrow & 12x+12& = &12+13+x \\\Leftrightarrow & 12x \color{red}{+12} & = &25 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &25-12 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x+7)& = & 2 \color{red}{-} (6+x) \\\Leftrightarrow & 12x+28& = &2-6-x \\\Leftrightarrow & 12x \color{red}{+28} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 12x+x& = &-4-28 \\\Leftrightarrow & 13x& = &-32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-32}{13} & & \\ & V = \left\{ \frac{-32}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+3)& = & 8 \color{red}{+} (13+x) \\\Leftrightarrow & -12x+12& = &8+13+x \\\Leftrightarrow & -12x \color{red}{+12} & = &21 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &21-12 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x+5)& = & 9 \color{red}{+} (-3+3x) \\\Leftrightarrow & 10x+25& = &9-3+3x \\\Leftrightarrow & 10x \color{red}{+25} & = &6 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-25} \\\Leftrightarrow & 10x-3x& = &6-25 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x+3)& = & 10 \color{red}{+} (-12-3x) \\\Leftrightarrow & 4x+12& = &10-12-3x \\\Leftrightarrow & 4x \color{red}{+12} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 4x+3x& = &-2-12 \\\Leftrightarrow & 7x& = &-14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-14}{ \color{red}{7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-4)& = & 7 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x-16& = &7+12-x \\\Leftrightarrow & -24x \color{red}{-16} & = &19 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -24x+x& = &19+16 \\\Leftrightarrow & -23x& = &35 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{35}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-35}{23} & & \\ & V = \left\{ \frac{-35}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+5)& = & 15 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+10& = &15+6+x \\\Leftrightarrow & -12x \color{red}{+10} & = &21 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -12x-x& = &21-10 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x-6)& = & 10 \color{red}{+} (1+x) \\\Leftrightarrow & -6x-12& = &10+1+x \\\Leftrightarrow & -6x \color{red}{-12} & = &11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &11+12 \\\Leftrightarrow & -7x& = &23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x+4)& = & 14 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x+16& = &14+12-x \\\Leftrightarrow & -12x \color{red}{+16} & = &26 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &26-16 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x+4)& = & 8 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x+12& = &8-15+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-7-12 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+5)& = & -2 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x+15& = &-2-5+x \\\Leftrightarrow & -12x \color{red}{+15} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -12x-x& = &-7-15 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)