Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x-1)& = & 1 \color{red}{-} (2+x) \\\Leftrightarrow & -20x-5& = &1-2-x \\\Leftrightarrow & -20x \color{red}{-5} & = &-1 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -20x+x& = &-1+5 \\\Leftrightarrow & -19x& = &4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x+4)& = & -12 \color{red}{+} (-1+x) \\\Leftrightarrow & -30x+20& = &-12-1+x \\\Leftrightarrow & -30x \color{red}{+20} & = &-13 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -30x-x& = &-13-20 \\\Leftrightarrow & -31x& = &-33 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-33}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{33}{31} & & \\ & V = \left\{ \frac{33}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x+1)& = & -15 \color{red}{+} (-10+x) \\\Leftrightarrow & -20x+5& = &-15-10+x \\\Leftrightarrow & -20x \color{red}{+5} & = &-25 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -20x-x& = &-25-5 \\\Leftrightarrow & -21x& = &-30 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-30}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x-6)& = & -9 \color{red}{-} (-5+x) \\\Leftrightarrow & -18x-36& = &-9+5-x \\\Leftrightarrow & -18x \color{red}{-36} & = &-4 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -18x+x& = &-4+36 \\\Leftrightarrow & -17x& = &32 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{32}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-32}{17} & & \\ & V = \left\{ \frac{-32}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-2)& = & -9 \color{red}{+} (-8-5x) \\\Leftrightarrow & -8x-8& = &-9-8-5x \\\Leftrightarrow & -8x \color{red}{-8} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & -8x+5x& = &-17+8 \\\Leftrightarrow & -3x& = &-9 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-9}{ \color{red}{-3} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+3)& = & 7 \color{red}{-} (-1-5x) \\\Leftrightarrow & 3x+9& = &7+1+5x \\\Leftrightarrow & 3x \color{red}{+9} & = &8 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 3x-5x& = &8-9 \\\Leftrightarrow & -2x& = &-1 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-1}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-1)& = & 13 \color{red}{-} (-15+x) \\\Leftrightarrow & 6x-6& = &13+15-x \\\Leftrightarrow & 6x \color{red}{-6} & = &28 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 6x+x& = &28+6 \\\Leftrightarrow & 7x& = &34 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{34}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{34}{7} & & \\ & V = \left\{ \frac{34}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-4)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & 12x-8& = &9+6+x \\\Leftrightarrow & 12x \color{red}{-8} & = &15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &15+8 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+2)& = & -3 \color{red}{+} (-7-5x) \\\Leftrightarrow & -36x+12& = &-3-7-5x \\\Leftrightarrow & -36x \color{red}{+12} & = &-10 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -36x+5x& = &-10-12 \\\Leftrightarrow & -31x& = &-22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x-5)& = & -10 \color{red}{+} (14+x) \\\Leftrightarrow & -20x-25& = &-10+14+x \\\Leftrightarrow & -20x \color{red}{-25} & = &4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -20x-x& = &4+25 \\\Leftrightarrow & -21x& = &29 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{29}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-29}{21} & & \\ & V = \left\{ \frac{-29}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-3)& = & 10 \color{red}{-} (-7+x) \\\Leftrightarrow & 8x-6& = &10+7-x \\\Leftrightarrow & 8x \color{red}{-6} & = &17 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 8x+x& = &17+6 \\\Leftrightarrow & 9x& = &23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{23}{9} & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-7)& = & 14 \color{red}{+} (-2+x) \\\Leftrightarrow & 30x-42& = &14-2+x \\\Leftrightarrow & 30x \color{red}{-42} & = &12 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &12+42 \\\Leftrightarrow & 29x& = &54 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{54}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{54}{29} & & \\ & V = \left\{ \frac{54}{29} \right\} & \\\end{align}\)