Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+5)& = & 7 \color{red}{+} (-5+3x) \\\Leftrightarrow & -4x+10& = &7-5+3x \\\Leftrightarrow & -4x \color{red}{+10} & = &2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -4x-3x& = &2-10 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+5)& = & -6 \color{red}{+} (-9+x) \\\Leftrightarrow & -10x+25& = &-6-9+x \\\Leftrightarrow & -10x \color{red}{+25} & = &-15 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -10x-x& = &-15-25 \\\Leftrightarrow & -11x& = &-40 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-40}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{40}{11} & & \\ & V = \left\{ \frac{40}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x+1)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & 24x+6& = &-6+13+x \\\Leftrightarrow & 24x \color{red}{+6} & = &7 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 24x-x& = &7-6 \\\Leftrightarrow & 23x& = &1 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{1}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+1)& = & 9 \color{red}{-} (-13-2x) \\\Leftrightarrow & -15x+5& = &9+13+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &22 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &22 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &22-5 \\\Leftrightarrow & -17x& = &17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{17}{ \color{red}{-17} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-7)& = & 12 \color{red}{+} (10+x) \\\Leftrightarrow & 30x-35& = &12+10+x \\\Leftrightarrow & 30x \color{red}{-35} & = &22 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 30x-x& = &22+35 \\\Leftrightarrow & 29x& = &57 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{57}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{57}{29} & & \\ & V = \left\{ \frac{57}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x-1)& = & 1 \color{red}{+} (13+x) \\\Leftrightarrow & 30x-6& = &1+13+x \\\Leftrightarrow & 30x \color{red}{-6} & = &14 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &14+6 \\\Leftrightarrow & 29x& = &20 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{20}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{20}{29} & & \\ & V = \left\{ \frac{20}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x-4)& = & -7 \color{red}{-} (14+x) \\\Leftrightarrow & -30x-24& = &-7-14-x \\\Leftrightarrow & -30x \color{red}{-24} & = &-21 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &-21+24 \\\Leftrightarrow & -29x& = &3 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{3}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-5)& = & 15 \color{red}{-} (-15+4x) \\\Leftrightarrow & -15x-15& = &15+15-4x \\\Leftrightarrow & -15x \color{red}{-15} & = &30 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &30 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -15x+4x& = &30+15 \\\Leftrightarrow & -11x& = &45 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{45}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-45}{11} & & \\ & V = \left\{ \frac{-45}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+5)& = & -10 \color{red}{+} (9+4x) \\\Leftrightarrow & 9x+15& = &-10+9+4x \\\Leftrightarrow & 9x \color{red}{+15} & = &-1 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 9x-4x& = &-1-15 \\\Leftrightarrow & 5x& = &-16 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-16}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-16}{5} & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x+1)& = & -14 \color{red}{+} (-8+3x) \\\Leftrightarrow & -10x+5& = &-14-8+3x \\\Leftrightarrow & -10x \color{red}{+5} & = &-22 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & -10x-3x& = &-22-5 \\\Leftrightarrow & -13x& = &-27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x+1)& = & -2 \color{red}{+} (2+x) \\\Leftrightarrow & -9x+3& = &-2+2+x \\\Leftrightarrow & -9x \color{red}{+3} & = &0 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -9x-x& = &0-3 \\\Leftrightarrow & -10x& = &-3 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-3}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x-6)& = & 12 \color{red}{+} (-11+x) \\\Leftrightarrow & 8x-24& = &12-11+x \\\Leftrightarrow & 8x \color{red}{-24} & = &1 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 8x-x& = &1+24 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)