Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (3x+6)& = & 9 \color{red}{+} (12-2x) \\\Leftrightarrow & 15x+30& = &9+12-2x \\\Leftrightarrow & 15x \color{red}{+30} & = &21 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &21 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & 15x+2x& = &21-30 \\\Leftrightarrow & 17x& = &-9 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-9}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+4)& = & -15 \color{red}{+} (5-2x) \\\Leftrightarrow & 5x+20& = &-15+5-2x \\\Leftrightarrow & 5x \color{red}{+20} & = &-10 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 5x+2x& = &-10-20 \\\Leftrightarrow & 7x& = &-30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+4)& = & -3 \color{red}{-} (-2+3x) \\\Leftrightarrow & -4x+8& = &-3+2-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &-1 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &-1-8 \\\Leftrightarrow & -x& = &-9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-9}{ \color{red}{-1} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x+3)& = & -14 \color{red}{+} (4+3x) \\\Leftrightarrow & -2x+6& = &-14+4+3x \\\Leftrightarrow & -2x \color{red}{+6} & = &-10 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -2x-3x& = &-10-6 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+4)& = & 4 \color{red}{-} (1+x) \\\Leftrightarrow & 12x+16& = &4-1-x \\\Leftrightarrow & 12x \color{red}{+16} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &3-16 \\\Leftrightarrow & 13x& = &-13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-13}{ \color{red}{13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x-4)& = & 12 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x-24& = &12-15+x \\\Leftrightarrow & 30x \color{red}{-24} & = &-3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 30x-x& = &-3+24 \\\Leftrightarrow & 29x& = &21 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{21}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{21}{29} & & \\ & V = \left\{ \frac{21}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x-1)& = & 12 \color{red}{-} (-3-3x) \\\Leftrightarrow & 10x-2& = &12+3+3x \\\Leftrightarrow & 10x \color{red}{-2} & = &15 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & 10x-3x& = &15+2 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x+7)& = & -8 \color{red}{+} (-3-5x) \\\Leftrightarrow & 6x+14& = &-8-3-5x \\\Leftrightarrow & 6x \color{red}{+14} & = &-11 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+14} \color{blue}{-14} \color{blue}{+5x} & = &-11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-14} \\\Leftrightarrow & 6x+5x& = &-11-14 \\\Leftrightarrow & 11x& = &-25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+3)& = & 2 \color{red}{+} (-12+x) \\\Leftrightarrow & 18x+18& = &2-12+x \\\Leftrightarrow & 18x \color{red}{+18} & = &-10 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 18x-x& = &-10-18 \\\Leftrightarrow & 17x& = &-28 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-28}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-28}{17} & & \\ & V = \left\{ \frac{-28}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x+3)& = & 2 \color{red}{-} (9-3x) \\\Leftrightarrow & -10x+15& = &2-9+3x \\\Leftrightarrow & -10x \color{red}{+15} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & -10x-3x& = &-7-15 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x-6)& = & 15 \color{red}{+} (-13-4x) \\\Leftrightarrow & 9x-18& = &15-13-4x \\\Leftrightarrow & 9x \color{red}{-18} & = &2 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & 9x+4x& = &2+18 \\\Leftrightarrow & 13x& = &20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x-5)& = & 3 \color{red}{+} (-10+x) \\\Leftrightarrow & -25x-25& = &3-10+x \\\Leftrightarrow & -25x \color{red}{-25} & = &-7 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -25x-x& = &-7+25 \\\Leftrightarrow & -26x& = &18 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{18}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)