Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x-4)& = & 3 \color{red}{-} (5-3x) \\\Leftrightarrow & 10x-8& = &3-5+3x \\\Leftrightarrow & 10x \color{red}{-8} & = &-2 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 10x-3x& = &-2+8 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (4x-7)& = & -6 \color{red}{-} (-13+x) \\\Leftrightarrow & 8x-14& = &-6+13-x \\\Leftrightarrow & 8x \color{red}{-14} & = &7 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 8x+x& = &7+14 \\\Leftrightarrow & 9x& = &21 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{21}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x+4)& = & 11 \color{red}{-} (15+4x) \\\Leftrightarrow & -9x+12& = &11-15-4x \\\Leftrightarrow & -9x \color{red}{+12} & = &-4 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & -9x+4x& = &-4-12 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-1)& = & 3 \color{red}{+} (10-5x) \\\Leftrightarrow & 16x-4& = &3+10-5x \\\Leftrightarrow & 16x \color{red}{-4} & = &13 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 16x+5x& = &13+4 \\\Leftrightarrow & 21x& = &17 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{17}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{17}{21} & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+6)& = & 14 \color{red}{-} (-13-5x) \\\Leftrightarrow & 6x+36& = &14+13+5x \\\Leftrightarrow & 6x \color{red}{+36} & = &27 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &27 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & 6x-5x& = &27-36 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x-4)& = & -12 \color{red}{+} (-11+4x) \\\Leftrightarrow & -15x-20& = &-12-11+4x \\\Leftrightarrow & -15x \color{red}{-20} & = &-23 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &-23 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -15x-4x& = &-23+20 \\\Leftrightarrow & -19x& = &-3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-5)& = & 1 \color{red}{+} (10-2x) \\\Leftrightarrow & -9x-15& = &1+10-2x \\\Leftrightarrow & -9x \color{red}{-15} & = &11 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -9x+2x& = &11+15 \\\Leftrightarrow & -7x& = &26 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{26}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-26}{7} & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x-4)& = & -10 \color{red}{+} (3+x) \\\Leftrightarrow & 8x-16& = &-10+3+x \\\Leftrightarrow & 8x \color{red}{-16} & = &-7 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 8x-x& = &-7+16 \\\Leftrightarrow & 7x& = &9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x-4)& = & 7 \color{red}{+} (15-5x) \\\Leftrightarrow & 6x-24& = &7+15-5x \\\Leftrightarrow & 6x \color{red}{-24} & = &22 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 6x+5x& = &22+24 \\\Leftrightarrow & 11x& = &46 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{46}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{46}{11} & & \\ & V = \left\{ \frac{46}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x-4)& = & 10 \color{red}{+} (6-5x) \\\Leftrightarrow & -6x-12& = &10+6-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &16 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &16+12 \\\Leftrightarrow & -x& = &28 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{28}{ \color{red}{-1} } \\\Leftrightarrow & x = -28 & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x-6)& = & -8 \color{red}{-} (11+x) \\\Leftrightarrow & 10x-30& = &-8-11-x \\\Leftrightarrow & 10x \color{red}{-30} & = &-19 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 10x+x& = &-19+30 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x-2)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & 25x-10& = &12-5-x \\\Leftrightarrow & 25x \color{red}{-10} & = &7 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 25x+x& = &7+10 \\\Leftrightarrow & 26x& = &17 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{17}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{17}{26} & & \\ & V = \left\{ \frac{17}{26} \right\} & \\\end{align}\)