Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+4)& = & -1 \color{red}{-} (-1+x) \\\Leftrightarrow & -2x+8& = &-1+1-x \\\Leftrightarrow & -2x \color{red}{+8} & = &0 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -2x+x& = &0-8 \\\Leftrightarrow & -x& = &-8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-8}{ \color{red}{-1} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+1)& = & 1 \color{red}{-} (-11+x) \\\Leftrightarrow & -8x+2& = &1+11-x \\\Leftrightarrow & -8x \color{red}{+2} & = &12 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -8x+x& = &12-2 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x-2)& = & -3 \color{red}{+} (-13+3x) \\\Leftrightarrow & 16x-8& = &-3-13+3x \\\Leftrightarrow & 16x \color{red}{-8} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 16x-3x& = &-16+8 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-3)& = & 9 \color{red}{+} (-10-5x) \\\Leftrightarrow & -6x-6& = &9-10-5x \\\Leftrightarrow & -6x \color{red}{-6} & = &-1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -6x+5x& = &-1+6 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+4)& = & -1 \color{red}{-} (11+x) \\\Leftrightarrow & -9x+12& = &-1-11-x \\\Leftrightarrow & -9x \color{red}{+12} & = &-12 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -9x+x& = &-12-12 \\\Leftrightarrow & -8x& = &-24 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-24}{ \color{red}{-8} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x-7)& = & -15 \color{red}{-} (12+x) \\\Leftrightarrow & 12x-28& = &-15-12-x \\\Leftrightarrow & 12x \color{red}{-28} & = &-27 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 12x+x& = &-27+28 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x+3)& = & 5 \color{red}{-} (5-3x) \\\Leftrightarrow & 10x+15& = &5-5+3x \\\Leftrightarrow & 10x \color{red}{+15} & = &0 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & 10x-3x& = &0-15 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x+5)& = & 11 \color{red}{-} (-14+x) \\\Leftrightarrow & -30x+25& = &11+14-x \\\Leftrightarrow & -30x \color{red}{+25} & = &25 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -30x+x& = &25-25 \\\Leftrightarrow & -29x& = &0 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{0}{ \color{red}{-29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-2)& = & -10 \color{red}{-} (7+x) \\\Leftrightarrow & 12x-12& = &-10-7-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-17 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-17+12 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x+6)& = & -4 \color{red}{-} (10+4x) \\\Leftrightarrow & -9x+18& = &-4-10-4x \\\Leftrightarrow & -9x \color{red}{+18} & = &-14 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{+4x} & = &-14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-18} \\\Leftrightarrow & -9x+4x& = &-14-18 \\\Leftrightarrow & -5x& = &-32 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-32}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\ & V = \left\{ \frac{32}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+5)& = & 9 \color{red}{-} (-8-2x) \\\Leftrightarrow & 9x+15& = &9+8+2x \\\Leftrightarrow & 9x \color{red}{+15} & = &17 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &17 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 9x-2x& = &17-15 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x-6)& = & 4 \color{red}{+} (-12+3x) \\\Leftrightarrow & -4x-24& = &4-12+3x \\\Leftrightarrow & -4x \color{red}{-24} & = &-8 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -4x-3x& = &-8+24 \\\Leftrightarrow & -7x& = &16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)