Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x-6)& = & 8 \color{red}{+} (6+x) \\\Leftrightarrow & 36x-36& = &8+6+x \\\Leftrightarrow & 36x \color{red}{-36} & = &14 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 36x-x& = &14+36 \\\Leftrightarrow & 35x& = &50 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{50}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+6)& = & -15 \color{red}{+} (14-5x) \\\Leftrightarrow & -6x+12& = &-15+14-5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -6x+5x& = &-1-12 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x+1)& = & -7 \color{red}{-} (-6-4x) \\\Leftrightarrow & 5x+5& = &-7+6+4x \\\Leftrightarrow & 5x \color{red}{+5} & = &-1 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 5x-4x& = &-1-5 \\\Leftrightarrow & x& = &-6 \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x+2)& = & -3 \color{red}{+} (3+x) \\\Leftrightarrow & 6x+12& = &-3+3+x \\\Leftrightarrow & 6x \color{red}{+12} & = &0 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &0-12 \\\Leftrightarrow & 5x& = &-12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x-7)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & 18x-42& = &2-2-x \\\Leftrightarrow & 18x \color{red}{-42} & = &0 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 18x+x& = &0+42 \\\Leftrightarrow & 19x& = &42 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{42}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{42}{19} & & \\ & V = \left\{ \frac{42}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x+2)& = & 12 \color{red}{+} (10+x) \\\Leftrightarrow & 20x+10& = &12+10+x \\\Leftrightarrow & 20x \color{red}{+10} & = &22 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 20x-x& = &22-10 \\\Leftrightarrow & 19x& = &12 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{12}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-1)& = & -5 \color{red}{-} (7+4x) \\\Leftrightarrow & -25x-5& = &-5-7-4x \\\Leftrightarrow & -25x \color{red}{-5} & = &-12 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &-12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & -25x+4x& = &-12+5 \\\Leftrightarrow & -21x& = &-7 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-7}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+6)& = & 7 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x+18& = &7+1-x \\\Leftrightarrow & -12x \color{red}{+18} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &8-18 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-5)& = & 3 \color{red}{+} (-10+3x) \\\Leftrightarrow & -4x-20& = &3-10+3x \\\Leftrightarrow & -4x \color{red}{-20} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -4x-3x& = &-7+20 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x+4)& = & -7 \color{red}{+} (-12+x) \\\Leftrightarrow & 2x+8& = &-7-12+x \\\Leftrightarrow & 2x \color{red}{+8} & = &-19 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 2x-x& = &-19-8 \\\Leftrightarrow & x& = &-27 \\ & V = \left\{ -27 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-5)& = & 6 \color{red}{+} (5-5x) \\\Leftrightarrow & -18x-15& = &6+5-5x \\\Leftrightarrow & -18x \color{red}{-15} & = &11 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -18x+5x& = &11+15 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x+3)& = & 11 \color{red}{-} (6-5x) \\\Leftrightarrow & -6x+9& = &11-6+5x \\\Leftrightarrow & -6x \color{red}{+9} & = &5 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & -6x-5x& = &5-9 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)