Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x+4)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -10x+20& = &3-14-x \\\Leftrightarrow & -10x \color{red}{+20} & = &-11 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -10x+x& = &-11-20 \\\Leftrightarrow & -9x& = &-31 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-31}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{31}{9} & & \\ & V = \left\{ \frac{31}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+4)& = & -9 \color{red}{-} (-1+3x) \\\Leftrightarrow & -25x+20& = &-9+1-3x \\\Leftrightarrow & -25x \color{red}{+20} & = &-8 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -25x+3x& = &-8-20 \\\Leftrightarrow & -22x& = &-28 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{-28}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x+1)& = & 6 \color{red}{-} (9+x) \\\Leftrightarrow & -10x+5& = &6-9-x \\\Leftrightarrow & -10x \color{red}{+5} & = &-3 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -10x+x& = &-3-5 \\\Leftrightarrow & -9x& = &-8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x+4)& = & 12 \color{red}{+} (-15-3x) \\\Leftrightarrow & -4x+16& = &12-15-3x \\\Leftrightarrow & -4x \color{red}{+16} & = &-3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & -4x+3x& = &-3-16 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x+2)& = & -15 \color{red}{-} (7+x) \\\Leftrightarrow & -36x+12& = &-15-7-x \\\Leftrightarrow & -36x \color{red}{+12} & = &-22 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -36x+x& = &-22-12 \\\Leftrightarrow & -35x& = &-34 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-34}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{34}{35} & & \\ & V = \left\{ \frac{34}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-1)& = & -14 \color{red}{+} (15+x) \\\Leftrightarrow & 30x-5& = &-14+15+x \\\Leftrightarrow & 30x \color{red}{-5} & = &1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 30x-x& = &1+5 \\\Leftrightarrow & 29x& = &6 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{6}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{6}{29} & & \\ & V = \left\{ \frac{6}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x+3)& = & -4 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x+9& = &-4+10-x \\\Leftrightarrow & 12x \color{red}{+9} & = &6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 12x+x& = &6-9 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x-5)& = & 14 \color{red}{-} (-11+x) \\\Leftrightarrow & 6x-15& = &14+11-x \\\Leftrightarrow & 6x \color{red}{-15} & = &25 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 6x+x& = &25+15 \\\Leftrightarrow & 7x& = &40 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{40}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{40}{7} & & \\ & V = \left\{ \frac{40}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x-4)& = & 11 \color{red}{-} (4+x) \\\Leftrightarrow & -20x-16& = &11-4-x \\\Leftrightarrow & -20x \color{red}{-16} & = &7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &7+16 \\\Leftrightarrow & -19x& = &23 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{23}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-23}{19} & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-1)& = & 3 \color{red}{+} (-15+x) \\\Leftrightarrow & 10x-5& = &3-15+x \\\Leftrightarrow & 10x \color{red}{-5} & = &-12 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 10x-x& = &-12+5 \\\Leftrightarrow & 9x& = &-7 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-7}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-7}{9} & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x-1)& = & -1 \color{red}{-} (12+3x) \\\Leftrightarrow & 16x-4& = &-1-12-3x \\\Leftrightarrow & 16x \color{red}{-4} & = &-13 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 16x+3x& = &-13+4 \\\Leftrightarrow & 19x& = &-9 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-9}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-9}{19} & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+2)& = & -2 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+12& = &-2-13-x \\\Leftrightarrow & 12x \color{red}{+12} & = &-15 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &-15-12 \\\Leftrightarrow & 13x& = &-27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)