Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x-7)& = & -8 \color{red}{-} (11+x) \\\Leftrightarrow & -30x-35& = &-8-11-x \\\Leftrightarrow & -30x \color{red}{-35} & = &-19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -30x+x& = &-19+35 \\\Leftrightarrow & -29x& = &16 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{16}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-16}{29} & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x-5)& = & -7 \color{red}{+} (-8-5x) \\\Leftrightarrow & -16x-20& = &-7-8-5x \\\Leftrightarrow & -16x \color{red}{-20} & = &-15 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-20} \color{blue}{+20} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+20} \\\Leftrightarrow & -16x+5x& = &-15+20 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (6x+7)& = & -10 \color{red}{-} (-9+x) \\\Leftrightarrow & 24x+28& = &-10+9-x \\\Leftrightarrow & 24x \color{red}{+28} & = &-1 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 24x+x& = &-1-28 \\\Leftrightarrow & 25x& = &-29 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-29}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-29}{25} & & \\ & V = \left\{ \frac{-29}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+7)& = & -11 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+21& = &-11+2-x \\\Leftrightarrow & -12x \color{red}{+21} & = &-9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &-9-21 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-7)& = & -10 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-14& = &-10+4+x \\\Leftrightarrow & 12x \color{red}{-14} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &-6+14 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+6)& = & -15 \color{red}{+} (1+x) \\\Leftrightarrow & 4x+12& = &-15+1+x \\\Leftrightarrow & 4x \color{red}{+12} & = &-14 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 4x-x& = &-14-12 \\\Leftrightarrow & 3x& = &-26 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-26}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-26}{3} & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x-2)& = & 9 \color{red}{+} (3+x) \\\Leftrightarrow & 25x-10& = &9+3+x \\\Leftrightarrow & 25x \color{red}{-10} & = &12 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 25x-x& = &12+10 \\\Leftrightarrow & 24x& = &22 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{22}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{11}{12} & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x-5)& = & 2 \color{red}{+} (-2+x) \\\Leftrightarrow & 6x-30& = &2-2+x \\\Leftrightarrow & 6x \color{red}{-30} & = &0 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 6x-x& = &0+30 \\\Leftrightarrow & 5x& = &30 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{30}{ \color{red}{5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x+5)& = & -11 \color{red}{-} (6+4x) \\\Leftrightarrow & -9x+15& = &-11-6-4x \\\Leftrightarrow & -9x \color{red}{+15} & = &-17 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -9x+4x& = &-17-15 \\\Leftrightarrow & -5x& = &-32 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-32}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\ & V = \left\{ \frac{32}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+6)& = & 6 \color{red}{+} (3+x) \\\Leftrightarrow & -24x+24& = &6+3+x \\\Leftrightarrow & -24x \color{red}{+24} & = &9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &9-24 \\\Leftrightarrow & -25x& = &-15 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-15}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+6)& = & -14 \color{red}{-} (8+x) \\\Leftrightarrow & -30x+36& = &-14-8-x \\\Leftrightarrow & -30x \color{red}{+36} & = &-22 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -30x+x& = &-22-36 \\\Leftrightarrow & -29x& = &-58 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-58}{ \color{red}{-29} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x+6)& = & 8 \color{red}{+} (14+x) \\\Leftrightarrow & 20x+30& = &8+14+x \\\Leftrightarrow & 20x \color{red}{+30} & = &22 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 20x-x& = &22-30 \\\Leftrightarrow & 19x& = &-8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)