Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+3)& = & 8 \color{red}{-} (15-5x) \\\Leftrightarrow & 6x+18& = &8-15+5x \\\Leftrightarrow & 6x \color{red}{+18} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 6x-5x& = &-7-18 \\\Leftrightarrow & x& = &-25 \\ & V = \left\{ -25 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-2)& = & -14 \color{red}{-} (14+x) \\\Leftrightarrow & -20x-10& = &-14-14-x \\\Leftrightarrow & -20x \color{red}{-10} & = &-28 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &-28+10 \\\Leftrightarrow & -19x& = &-18 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-18}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+7)& = & 1 \color{red}{-} (8+x) \\\Leftrightarrow & 4x+14& = &1-8-x \\\Leftrightarrow & 4x \color{red}{+14} & = &-7 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 4x+x& = &-7-14 \\\Leftrightarrow & 5x& = &-21 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-21}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-5)& = & 14 \color{red}{-} (4+3x) \\\Leftrightarrow & 2x-10& = &14-4-3x \\\Leftrightarrow & 2x \color{red}{-10} & = &10 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 2x+3x& = &10+10 \\\Leftrightarrow & 5x& = &20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{20}{ \color{red}{5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x+5)& = & -8 \color{red}{+} (7+x) \\\Leftrightarrow & -20x+25& = &-8+7+x \\\Leftrightarrow & -20x \color{red}{+25} & = &-1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &-1-25 \\\Leftrightarrow & -21x& = &-26 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-26}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x-7)& = & -3 \color{red}{+} (-9+x) \\\Leftrightarrow & 2x-14& = &-3-9+x \\\Leftrightarrow & 2x \color{red}{-14} & = &-12 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 2x-x& = &-12+14 \\\Leftrightarrow & x& = &2 \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x-4)& = & 10 \color{red}{-} (8+x) \\\Leftrightarrow & 16x-16& = &10-8-x \\\Leftrightarrow & 16x \color{red}{-16} & = &2 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 16x+x& = &2+16 \\\Leftrightarrow & 17x& = &18 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{18}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+1)& = & 2 \color{red}{-} (-10-5x) \\\Leftrightarrow & 18x+3& = &2+10+5x \\\Leftrightarrow & 18x \color{red}{+3} & = &12 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & 18x-5x& = &12-3 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-3)& = & 1 \color{red}{+} (-10+x) \\\Leftrightarrow & 20x-15& = &1-10+x \\\Leftrightarrow & 20x \color{red}{-15} & = &-9 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 20x-x& = &-9+15 \\\Leftrightarrow & 19x& = &6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{6}{19} & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x-7)& = & -4 \color{red}{+} (8+4x) \\\Leftrightarrow & 3x-21& = &-4+8+4x \\\Leftrightarrow & 3x \color{red}{-21} & = &4 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & 3x-4x& = &4+21 \\\Leftrightarrow & -x& = &25 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{25}{ \color{red}{-1} } \\\Leftrightarrow & x = -25 & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-7)& = & 7 \color{red}{+} (-15+x) \\\Leftrightarrow & -24x-28& = &7-15+x \\\Leftrightarrow & -24x \color{red}{-28} & = &-8 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -24x-x& = &-8+28 \\\Leftrightarrow & -25x& = &20 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{20}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+3)& = & -4 \color{red}{-} (7+x) \\\Leftrightarrow & 25x+15& = &-4-7-x \\\Leftrightarrow & 25x \color{red}{+15} & = &-11 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 25x+x& = &-11-15 \\\Leftrightarrow & 26x& = &-26 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-26}{ \color{red}{26} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)