Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+1)& = & 12 \color{red}{+} (-5+x) \\\Leftrightarrow & 18x+3& = &12-5+x \\\Leftrightarrow & 18x \color{red}{+3} & = &7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 18x-x& = &7-3 \\\Leftrightarrow & 17x& = &4 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{4}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{4}{17} & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+1)& = & 9 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+4& = &9+4+x \\\Leftrightarrow & 12x \color{red}{+4} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &13-4 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-1)& = & -1 \color{red}{-} (3-4x) \\\Leftrightarrow & 25x-5& = &-1-3+4x \\\Leftrightarrow & 25x \color{red}{-5} & = &-4 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &-4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & 25x-4x& = &-4+5 \\\Leftrightarrow & 21x& = &1 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{1}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x-5)& = & 7 \color{red}{+} (-2+x) \\\Leftrightarrow & 24x-20& = &7-2+x \\\Leftrightarrow & 24x \color{red}{-20} & = &5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &5+20 \\\Leftrightarrow & 23x& = &25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x-6)& = & 6 \color{red}{+} (10-3x) \\\Leftrightarrow & 4x-12& = &6+10-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &16 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &16+12 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-6)& = & 8 \color{red}{+} (-12+x) \\\Leftrightarrow & 18x-18& = &8-12+x \\\Leftrightarrow & 18x \color{red}{-18} & = &-4 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &-4+18 \\\Leftrightarrow & 17x& = &14 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{14}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{14}{17} & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-7)& = & -9 \color{red}{+} (-15+x) \\\Leftrightarrow & 20x-35& = &-9-15+x \\\Leftrightarrow & 20x \color{red}{-35} & = &-24 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 20x-x& = &-24+35 \\\Leftrightarrow & 19x& = &11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x+4)& = & -11 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+24& = &-11-4+x \\\Leftrightarrow & -12x \color{red}{+24} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -12x-x& = &-15-24 \\\Leftrightarrow & -13x& = &-39 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-39}{ \color{red}{-13} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x+2)& = & -6 \color{red}{+} (1+x) \\\Leftrightarrow & 4x+4& = &-6+1+x \\\Leftrightarrow & 4x \color{red}{+4} & = &-5 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 4x-x& = &-5-4 \\\Leftrightarrow & 3x& = &-9 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-9}{ \color{red}{3} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+2)& = & 14 \color{red}{-} (-1+x) \\\Leftrightarrow & -18x+6& = &14+1-x \\\Leftrightarrow & -18x \color{red}{+6} & = &15 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -18x+x& = &15-6 \\\Leftrightarrow & -17x& = &9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x+3)& = & 14 \color{red}{+} (-14+x) \\\Leftrightarrow & -18x+18& = &14-14+x \\\Leftrightarrow & -18x \color{red}{+18} & = &0 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -18x-x& = &0-18 \\\Leftrightarrow & -19x& = &-18 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-18}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-1)& = & -11 \color{red}{+} (-6-3x) \\\Leftrightarrow & -4x-2& = &-11-6-3x \\\Leftrightarrow & -4x \color{red}{-2} & = &-17 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -4x+3x& = &-17+2 \\\Leftrightarrow & -x& = &-15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-15}{ \color{red}{-1} } \\\Leftrightarrow & x = 15 & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)