Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x-5)& = & 11 \color{red}{-} (11+x) \\\Leftrightarrow & 24x-30& = &11-11-x \\\Leftrightarrow & 24x \color{red}{-30} & = &0 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &0+30 \\\Leftrightarrow & 25x& = &30 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{30}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+5)& = & -13 \color{red}{+} (6+x) \\\Leftrightarrow & -24x+30& = &-13+6+x \\\Leftrightarrow & -24x \color{red}{+30} & = &-7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &-7-30 \\\Leftrightarrow & -25x& = &-37 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-37}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{37}{25} & & \\ & V = \left\{ \frac{37}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x+6)& = & -1 \color{red}{-} (-3+2x) \\\Leftrightarrow & -15x+18& = &-1+3-2x \\\Leftrightarrow & -15x \color{red}{+18} & = &2 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & -15x+2x& = &2-18 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+6)& = & -14 \color{red}{+} (-5+x) \\\Leftrightarrow & 6x+18& = &-14-5+x \\\Leftrightarrow & 6x \color{red}{+18} & = &-19 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 6x-x& = &-19-18 \\\Leftrightarrow & 5x& = &-37 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-37}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-37}{5} & & \\ & V = \left\{ \frac{-37}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x+7)& = & -6 \color{red}{-} (-3+x) \\\Leftrightarrow & 18x+42& = &-6+3-x \\\Leftrightarrow & 18x \color{red}{+42} & = &-3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 18x+x& = &-3-42 \\\Leftrightarrow & 19x& = &-45 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-45}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-45}{19} & & \\ & V = \left\{ \frac{-45}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x+4)& = & -9 \color{red}{-} (-9+3x) \\\Leftrightarrow & -4x+8& = &-9+9-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &0 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &0-8 \\\Leftrightarrow & -x& = &-8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-8}{ \color{red}{-1} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x-5)& = & 5 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-20& = &5-3+x \\\Leftrightarrow & -12x \color{red}{-20} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -12x-x& = &2+20 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+5)& = & -10 \color{red}{+} (8+x) \\\Leftrightarrow & 20x+20& = &-10+8+x \\\Leftrightarrow & 20x \color{red}{+20} & = &-2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &-2-20 \\\Leftrightarrow & 19x& = &-22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-22}{19} & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x+1)& = & -7 \color{red}{+} (-8-2x) \\\Leftrightarrow & -15x+3& = &-7-8-2x \\\Leftrightarrow & -15x \color{red}{+3} & = &-15 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &-15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & -15x+2x& = &-15-3 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x-7)& = & -8 \color{red}{-} (6-2x) \\\Leftrightarrow & 3x-21& = &-8-6+2x \\\Leftrightarrow & 3x \color{red}{-21} & = &-14 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &-14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & 3x-2x& = &-14+21 \\\Leftrightarrow & x& = &7 \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x+6)& = & 15 \color{red}{+} (4-5x) \\\Leftrightarrow & 6x+36& = &15+4-5x \\\Leftrightarrow & 6x \color{red}{+36} & = &19 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 6x+5x& = &19-36 \\\Leftrightarrow & 11x& = &-17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x-5)& = & 7 \color{red}{+} (-11+x) \\\Leftrightarrow & 20x-25& = &7-11+x \\\Leftrightarrow & 20x \color{red}{-25} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 20x-x& = &-4+25 \\\Leftrightarrow & 19x& = &21 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{21}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{21}{19} & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)