Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+4)& = & 15 \color{red}{+} (15-5x) \\\Leftrightarrow & -6x+24& = &15+15-5x \\\Leftrightarrow & -6x \color{red}{+24} & = &30 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &30 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -6x+5x& = &30-24 \\\Leftrightarrow & -x& = &6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{6}{ \color{red}{-1} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x-5)& = & -11 \color{red}{+} (-8+x) \\\Leftrightarrow & 2x-10& = &-11-8+x \\\Leftrightarrow & 2x \color{red}{-10} & = &-19 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 2x-x& = &-19+10 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-1)& = & -3 \color{red}{-} (2+x) \\\Leftrightarrow & -2x-2& = &-3-2-x \\\Leftrightarrow & -2x \color{red}{-2} & = &-5 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -2x+x& = &-5+2 \\\Leftrightarrow & -x& = &-3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-3}{ \color{red}{-1} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-2)& = & 1 \color{red}{+} (12-5x) \\\Leftrightarrow & -6x-12& = &1+12-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &13 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &13+12 \\\Leftrightarrow & -x& = &25 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{25}{ \color{red}{-1} } \\\Leftrightarrow & x = -25 & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x+2)& = & -15 \color{red}{-} (8+x) \\\Leftrightarrow & 12x+4& = &-15-8-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-23 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-23-4 \\\Leftrightarrow & 13x& = &-27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+1)& = & -7 \color{red}{+} (-12-3x) \\\Leftrightarrow & 4x+2& = &-7-12-3x \\\Leftrightarrow & 4x \color{red}{+2} & = &-19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 4x+3x& = &-19-2 \\\Leftrightarrow & 7x& = &-21 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-21}{ \color{red}{7} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x+4)& = & -6 \color{red}{-} (6-5x) \\\Leftrightarrow & 6x+24& = &-6-6+5x \\\Leftrightarrow & 6x \color{red}{+24} & = &-12 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 6x-5x& = &-12-24 \\\Leftrightarrow & x& = &-36 \\ & V = \left\{ -36 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x+1)& = & -15 \color{red}{-} (-8-3x) \\\Leftrightarrow & 4x+4& = &-15+8+3x \\\Leftrightarrow & 4x \color{red}{+4} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 4x-3x& = &-7-4 \\\Leftrightarrow & x& = &-11 \\ & V = \left\{ -11 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+5)& = & -6 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+15& = &-6+5-x \\\Leftrightarrow & -12x \color{red}{+15} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &-1-15 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+4)& = & -2 \color{red}{-} (10-5x) \\\Leftrightarrow & -16x+16& = &-2-10+5x \\\Leftrightarrow & -16x \color{red}{+16} & = &-12 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & -16x-5x& = &-12-16 \\\Leftrightarrow & -21x& = &-28 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-28}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x-6)& = & 10 \color{red}{+} (-10+x) \\\Leftrightarrow & 4x-12& = &10-10+x \\\Leftrightarrow & 4x \color{red}{-12} & = &0 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 4x-x& = &0+12 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x-1)& = & 4 \color{red}{+} (-13-2x) \\\Leftrightarrow & 15x-5& = &4-13-2x \\\Leftrightarrow & 15x \color{red}{-5} & = &-9 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 15x+2x& = &-9+5 \\\Leftrightarrow & 17x& = &-4 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-4}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)