Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x-7)& = & 5 \color{red}{-} (1-5x) \\\Leftrightarrow & 6x-42& = &5-1+5x \\\Leftrightarrow & 6x \color{red}{-42} & = &4 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 6x-5x& = &4+42 \\\Leftrightarrow & x& = &46 \\ & V = \left\{ 46 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x+3)& = & 7 \color{red}{-} (7-5x) \\\Leftrightarrow & 16x+12& = &7-7+5x \\\Leftrightarrow & 16x \color{red}{+12} & = &0 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 16x-5x& = &0-12 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+5)& = & -13 \color{red}{+} (-12+x) \\\Leftrightarrow & 25x+25& = &-13-12+x \\\Leftrightarrow & 25x \color{red}{+25} & = &-25 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 25x-x& = &-25-25 \\\Leftrightarrow & 24x& = &-50 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-50}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-25}{12} & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x-7)& = & 1 \color{red}{-} (14+3x) \\\Leftrightarrow & -4x-28& = &1-14-3x \\\Leftrightarrow & -4x \color{red}{-28} & = &-13 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -4x+3x& = &-13+28 \\\Leftrightarrow & -x& = &15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{15}{ \color{red}{-1} } \\\Leftrightarrow & x = -15 & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-5)& = & -5 \color{red}{+} (-8+3x) \\\Leftrightarrow & -25x-25& = &-5-8+3x \\\Leftrightarrow & -25x \color{red}{-25} & = &-13 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -25x-3x& = &-13+25 \\\Leftrightarrow & -28x& = &12 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{12}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x-1)& = & 3 \color{red}{+} (10+x) \\\Leftrightarrow & 6x-6& = &3+10+x \\\Leftrightarrow & 6x \color{red}{-6} & = &13 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 6x-x& = &13+6 \\\Leftrightarrow & 5x& = &19 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{19}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x+5)& = & -10 \color{red}{-} (-10+x) \\\Leftrightarrow & -30x+30& = &-10+10-x \\\Leftrightarrow & -30x \color{red}{+30} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &0-30 \\\Leftrightarrow & -29x& = &-30 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-30}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{30}{29} & & \\ & V = \left\{ \frac{30}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x+5)& = & -11 \color{red}{+} (9+x) \\\Leftrightarrow & -6x+15& = &-11+9+x \\\Leftrightarrow & -6x \color{red}{+15} & = &-2 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -6x-x& = &-2-15 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x-3)& = & 4 \color{red}{-} (-4+2x) \\\Leftrightarrow & 15x-9& = &4+4-2x \\\Leftrightarrow & 15x \color{red}{-9} & = &8 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & 15x+2x& = &8+9 \\\Leftrightarrow & 17x& = &17 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{17}{ \color{red}{17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+6)& = & 1 \color{red}{-} (-13+4x) \\\Leftrightarrow & 15x+30& = &1+13-4x \\\Leftrightarrow & 15x \color{red}{+30} & = &14 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 15x+4x& = &14-30 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-2x-3)& = & -3 \color{red}{-} (-2+3x) \\\Leftrightarrow & -10x-15& = &-3+2-3x \\\Leftrightarrow & -10x \color{red}{-15} & = &-1 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & -10x+3x& = &-1+15 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x+4)& = & -14 \color{red}{-} (9-4x) \\\Leftrightarrow & -9x+12& = &-14-9+4x \\\Leftrightarrow & -9x \color{red}{+12} & = &-23 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &-23 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & -9x-4x& = &-23-12 \\\Leftrightarrow & -13x& = &-35 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-35}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)