Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+2)& = & 10 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x+12& = &10+2-x \\\Leftrightarrow & -30x \color{red}{+12} & = &12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &12-12 \\\Leftrightarrow & -29x& = &0 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{0}{ \color{red}{-29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x-2)& = & -5 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-4& = &-5-7-x \\\Leftrightarrow & -12x \color{red}{-4} & = &-12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &-12+4 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x-7)& = & 15 \color{red}{-} (5+4x) \\\Leftrightarrow & -15x-35& = &15-5-4x \\\Leftrightarrow & -15x \color{red}{-35} & = &10 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & -15x+4x& = &10+35 \\\Leftrightarrow & -11x& = &45 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{45}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-45}{11} & & \\ & V = \left\{ \frac{-45}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-7)& = & -3 \color{red}{+} (15+x) \\\Leftrightarrow & 4x-28& = &-3+15+x \\\Leftrightarrow & 4x \color{red}{-28} & = &12 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 4x-x& = &12+28 \\\Leftrightarrow & 3x& = &40 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{40}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{40}{3} & & \\ & V = \left\{ \frac{40}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x-2)& = & 3 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x-8& = &3+12-x \\\Leftrightarrow & -12x \color{red}{-8} & = &15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -12x+x& = &15+8 \\\Leftrightarrow & -11x& = &23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x-5)& = & -11 \color{red}{+} (-5+x) \\\Leftrightarrow & -4x-10& = &-11-5+x \\\Leftrightarrow & -4x \color{red}{-10} & = &-16 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &-16+10 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-3)& = & -13 \color{red}{-} (5+x) \\\Leftrightarrow & -5x-15& = &-13-5-x \\\Leftrightarrow & -5x \color{red}{-15} & = &-18 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -5x+x& = &-18+15 \\\Leftrightarrow & -4x& = &-3 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-3}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-2)& = & 8 \color{red}{+} (-9-4x) \\\Leftrightarrow & -9x-6& = &8-9-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &-1 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &-1+6 \\\Leftrightarrow & -5x& = &5 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{5}{ \color{red}{-5} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x-7)& = & -6 \color{red}{-} (-11+x) \\\Leftrightarrow & 6x-21& = &-6+11-x \\\Leftrightarrow & 6x \color{red}{-21} & = &5 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 6x+x& = &5+21 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (3x-5)& = & 14 \color{red}{+} (-1+x) \\\Leftrightarrow & 18x-30& = &14-1+x \\\Leftrightarrow & 18x \color{red}{-30} & = &13 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 18x-x& = &13+30 \\\Leftrightarrow & 17x& = &43 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{43}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{43}{17} & & \\ & V = \left\{ \frac{43}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x-2)& = & -11 \color{red}{-} (-13+x) \\\Leftrightarrow & 16x-8& = &-11+13-x \\\Leftrightarrow & 16x \color{red}{-8} & = &2 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 16x+x& = &2+8 \\\Leftrightarrow & 17x& = &10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x-4)& = & 2 \color{red}{-} (-8+x) \\\Leftrightarrow & 8x-16& = &2+8-x \\\Leftrightarrow & 8x \color{red}{-16} & = &10 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 8x+x& = &10+16 \\\Leftrightarrow & 9x& = &26 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{26}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{26}{9} & & \\ & V = \left\{ \frac{26}{9} \right\} & \\\end{align}\)