Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x+1)& = & -12 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+3& = &-12-13-x \\\Leftrightarrow & 12x \color{red}{+3} & = &-25 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &-25-3 \\\Leftrightarrow & 13x& = &-28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+3)& = & -9 \color{red}{+} (-2+x) \\\Leftrightarrow & -6x+6& = &-9-2+x \\\Leftrightarrow & -6x \color{red}{+6} & = &-11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &-11-6 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x-4)& = & 7 \color{red}{+} (1-3x) \\\Leftrightarrow & -10x-8& = &7+1-3x \\\Leftrightarrow & -10x \color{red}{-8} & = &8 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -10x+3x& = &8+8 \\\Leftrightarrow & -7x& = &16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x-7)& = & -15 \color{red}{+} (5+x) \\\Leftrightarrow & -18x-21& = &-15+5+x \\\Leftrightarrow & -18x \color{red}{-21} & = &-10 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -18x-x& = &-10+21 \\\Leftrightarrow & -19x& = &11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x+1)& = & -5 \color{red}{-} (7-5x) \\\Leftrightarrow & 18x+6& = &-5-7+5x \\\Leftrightarrow & 18x \color{red}{+6} & = &-12 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 18x-5x& = &-12-6 \\\Leftrightarrow & 13x& = &-18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x-1)& = & -3 \color{red}{-} (4-5x) \\\Leftrightarrow & -6x-3& = &-3-4+5x \\\Leftrightarrow & -6x \color{red}{-3} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -6x-5x& = &-7+3 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x+2)& = & 9 \color{red}{-} (11-5x) \\\Leftrightarrow & -6x+4& = &9-11+5x \\\Leftrightarrow & -6x \color{red}{+4} & = &-2 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & -6x-5x& = &-2-4 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x-2)& = & 4 \color{red}{+} (-14+3x) \\\Leftrightarrow & 20x-10& = &4-14+3x \\\Leftrightarrow & 20x \color{red}{-10} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 20x-3x& = &-10+10 \\\Leftrightarrow & 17x& = &0 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{0}{ \color{red}{17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x+7)& = & 13 \color{red}{-} (-6+x) \\\Leftrightarrow & 20x+35& = &13+6-x \\\Leftrightarrow & 20x \color{red}{+35} & = &19 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 20x+x& = &19-35 \\\Leftrightarrow & 21x& = &-16 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-16}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-16}{21} & & \\ & V = \left\{ \frac{-16}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x+3)& = & 3 \color{red}{+} (-8-3x) \\\Leftrightarrow & 4x+12& = &3-8-3x \\\Leftrightarrow & 4x \color{red}{+12} & = &-5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 4x+3x& = &-5-12 \\\Leftrightarrow & 7x& = &-17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x+7)& = & 10 \color{red}{+} (-8-5x) \\\Leftrightarrow & 18x+21& = &10-8-5x \\\Leftrightarrow & 18x \color{red}{+21} & = &2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & 18x+5x& = &2-21 \\\Leftrightarrow & 23x& = &-19 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-19}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-19}{23} & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+6)& = & 9 \color{red}{-} (-14+x) \\\Leftrightarrow & 4x+24& = &9+14-x \\\Leftrightarrow & 4x \color{red}{+24} & = &23 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 4x+x& = &23-24 \\\Leftrightarrow & 5x& = &-1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)