Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-1)& = & 10 \color{red}{-} (-4+x) \\\Leftrightarrow & 16x-4& = &10+4-x \\\Leftrightarrow & 16x \color{red}{-4} & = &14 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 16x+x& = &14+4 \\\Leftrightarrow & 17x& = &18 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{18}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+1)& = & 1 \color{red}{+} (13-5x) \\\Leftrightarrow & 8x+4& = &1+13-5x \\\Leftrightarrow & 8x \color{red}{+4} & = &14 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & 8x+5x& = &14-4 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+4)& = & -12 \color{red}{+} (-7+x) \\\Leftrightarrow & 20x+16& = &-12-7+x \\\Leftrightarrow & 20x \color{red}{+16} & = &-19 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &-19-16 \\\Leftrightarrow & 19x& = &-35 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-35}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-35}{19} & & \\ & V = \left\{ \frac{-35}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x+7)& = & 15 \color{red}{-} (-12+x) \\\Leftrightarrow & -6x+42& = &15+12-x \\\Leftrightarrow & -6x \color{red}{+42} & = &27 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -6x+x& = &27-42 \\\Leftrightarrow & -5x& = &-15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-15}{ \color{red}{-5} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x+3)& = & 12 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x+12& = &12-3+x \\\Leftrightarrow & -20x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -20x-x& = &9-12 \\\Leftrightarrow & -21x& = &-3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x-5)& = & -5 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x-30& = &-5-14+x \\\Leftrightarrow & -12x \color{red}{-30} & = &-19 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -12x-x& = &-19+30 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x-2)& = & 1 \color{red}{+} (-10+x) \\\Leftrightarrow & 10x-4& = &1-10+x \\\Leftrightarrow & 10x \color{red}{-4} & = &-9 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 10x-x& = &-9+4 \\\Leftrightarrow & 9x& = &-5 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-5}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-5}{9} & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x+5)& = & -7 \color{red}{-} (-3+3x) \\\Leftrightarrow & -4x+20& = &-7+3-3x \\\Leftrightarrow & -4x \color{red}{+20} & = &-4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -4x+3x& = &-4-20 \\\Leftrightarrow & -x& = &-24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-24}{ \color{red}{-1} } \\\Leftrightarrow & x = 24 & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x+7)& = & 12 \color{red}{+} (-12-3x) \\\Leftrightarrow & 10x+14& = &12-12-3x \\\Leftrightarrow & 10x \color{red}{+14} & = &0 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 10x+3x& = &0-14 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+2)& = & 8 \color{red}{+} (15-5x) \\\Leftrightarrow & -18x+6& = &8+15-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &23 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &23-6 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+2)& = & 6 \color{red}{-} (12+x) \\\Leftrightarrow & -8x+4& = &6-12-x \\\Leftrightarrow & -8x \color{red}{+4} & = &-6 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -8x+x& = &-6-4 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x+1)& = & 7 \color{red}{-} (9+x) \\\Leftrightarrow & -24x+6& = &7-9-x \\\Leftrightarrow & -24x \color{red}{+6} & = &-2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &-2-6 \\\Leftrightarrow & -23x& = &-8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)