Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+1)& = & -10 \color{red}{+} (-13+x) \\\Leftrightarrow & -6x+6& = &-10-13+x \\\Leftrightarrow & -6x \color{red}{+6} & = &-23 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &-23-6 \\\Leftrightarrow & -7x& = &-29 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-29}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x-5)& = & 6 \color{red}{+} (6+x) \\\Leftrightarrow & 12x-30& = &6+6+x \\\Leftrightarrow & 12x \color{red}{-30} & = &12 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &12+30 \\\Leftrightarrow & 11x& = &42 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{42}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{42}{11} & & \\ & V = \left\{ \frac{42}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x+1)& = & -1 \color{red}{-} (-6-4x) \\\Leftrightarrow & -25x+5& = &-1+6+4x \\\Leftrightarrow & -25x \color{red}{+5} & = &5 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & -25x-4x& = &5-5 \\\Leftrightarrow & -29x& = &0 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{0}{ \color{red}{-29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x-2)& = & -5 \color{red}{-} (-12+x) \\\Leftrightarrow & -20x-10& = &-5+12-x \\\Leftrightarrow & -20x \color{red}{-10} & = &7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &7+10 \\\Leftrightarrow & -19x& = &17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x-1)& = & -2 \color{red}{-} (-9-2x) \\\Leftrightarrow & 5x-5& = &-2+9+2x \\\Leftrightarrow & 5x \color{red}{-5} & = &7 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 5x-2x& = &7+5 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x-7)& = & 7 \color{red}{-} (9-3x) \\\Leftrightarrow & -16x-28& = &7-9+3x \\\Leftrightarrow & -16x \color{red}{-28} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -16x-3x& = &-2+28 \\\Leftrightarrow & -19x& = &26 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{26}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-26}{19} & & \\ & V = \left\{ \frac{-26}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x+2)& = & -6 \color{red}{-} (5+x) \\\Leftrightarrow & -20x+10& = &-6-5-x \\\Leftrightarrow & -20x \color{red}{+10} & = &-11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -20x+x& = &-11-10 \\\Leftrightarrow & -19x& = &-21 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-21}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{21}{19} & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x+1)& = & 3 \color{red}{+} (5+x) \\\Leftrightarrow & -12x+6& = &3+5+x \\\Leftrightarrow & -12x \color{red}{+6} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &8-6 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x+5)& = & 11 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x+10& = &11+12-x \\\Leftrightarrow & 12x \color{red}{+10} & = &23 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 12x+x& = &23-10 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x+5)& = & 15 \color{red}{-} (15+3x) \\\Leftrightarrow & -25x+25& = &15-15-3x \\\Leftrightarrow & -25x \color{red}{+25} & = &0 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & -25x+3x& = &0-25 \\\Leftrightarrow & -22x& = &-25 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{-25}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{25}{22} & & \\ & V = \left\{ \frac{25}{22} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x-7)& = & -3 \color{red}{+} (-1+x) \\\Leftrightarrow & 4x-28& = &-3-1+x \\\Leftrightarrow & 4x \color{red}{-28} & = &-4 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 4x-x& = &-4+28 \\\Leftrightarrow & 3x& = &24 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{24}{ \color{red}{3} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x+1)& = & -4 \color{red}{-} (5-3x) \\\Leftrightarrow & -4x+4& = &-4-5+3x \\\Leftrightarrow & -4x \color{red}{+4} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -4x-3x& = &-9-4 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)