Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x+4)& = & 5 \color{red}{+} (10-5x) \\\Leftrightarrow & 6x+8& = &5+10-5x \\\Leftrightarrow & 6x \color{red}{+8} & = &15 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & 6x+5x& = &15-8 \\\Leftrightarrow & 11x& = &7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x+1)& = & -8 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x+6& = &-8-1+x \\\Leftrightarrow & 30x \color{red}{+6} & = &-9 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 30x-x& = &-9-6 \\\Leftrightarrow & 29x& = &-15 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-15}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-15}{29} & & \\ & V = \left\{ \frac{-15}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+4)& = & -10 \color{red}{-} (14+3x) \\\Leftrightarrow & 4x+8& = &-10-14-3x \\\Leftrightarrow & 4x \color{red}{+8} & = &-24 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 4x+3x& = &-24-8 \\\Leftrightarrow & 7x& = &-32 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-32}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-32}{7} & & \\ & V = \left\{ \frac{-32}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+4)& = & -7 \color{red}{+} (-11-5x) \\\Leftrightarrow & 6x+12& = &-7-11-5x \\\Leftrightarrow & 6x \color{red}{+12} & = &-18 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 6x+5x& = &-18-12 \\\Leftrightarrow & 11x& = &-30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+6)& = & 1 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x+24& = &1-11+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-10-24 \\\Leftrightarrow & 11x& = &-34 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-34}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-34}{11} & & \\ & V = \left\{ \frac{-34}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x+7)& = & 2 \color{red}{+} (14+x) \\\Leftrightarrow & 2x+14& = &2+14+x \\\Leftrightarrow & 2x \color{red}{+14} & = &16 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 2x-x& = &16-14 \\\Leftrightarrow & x& = &2 \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x-6)& = & -2 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x-36& = &-2-4+x \\\Leftrightarrow & -24x \color{red}{-36} & = &-6 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -24x-x& = &-6+36 \\\Leftrightarrow & -25x& = &30 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{30}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x-7)& = & 12 \color{red}{+} (6+x) \\\Leftrightarrow & 24x-28& = &12+6+x \\\Leftrightarrow & 24x \color{red}{-28} & = &18 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 24x-x& = &18+28 \\\Leftrightarrow & 23x& = &46 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{46}{ \color{red}{23} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-6)& = & -9 \color{red}{-} (-14-3x) \\\Leftrightarrow & 4x-12& = &-9+14+3x \\\Leftrightarrow & 4x \color{red}{-12} & = &5 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 4x-3x& = &5+12 \\\Leftrightarrow & x& = &17 \\ & V = \left\{ 17 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-7)& = & -15 \color{red}{+} (-13+x) \\\Leftrightarrow & -4x-28& = &-15-13+x \\\Leftrightarrow & -4x \color{red}{-28} & = &-28 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-28 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -4x-x& = &-28+28 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-1)& = & 9 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x-6& = &9-12+x \\\Leftrightarrow & -12x \color{red}{-6} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &-3+6 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x-6)& = & 3 \color{red}{-} (-7+x) \\\Leftrightarrow & -24x-24& = &3+7-x \\\Leftrightarrow & -24x \color{red}{-24} & = &10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &10+24 \\\Leftrightarrow & -23x& = &34 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{34}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-34}{23} & & \\ & V = \left\{ \frac{-34}{23} \right\} & \\\end{align}\)