Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+6)& = & 5 \color{red}{-} (-6+x) \\\Leftrightarrow & 20x+30& = &5+6-x \\\Leftrightarrow & 20x \color{red}{+30} & = &11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 20x+x& = &11-30 \\\Leftrightarrow & 21x& = &-19 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-19}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-19}{21} & & \\ & V = \left\{ \frac{-19}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x-1)& = & -10 \color{red}{+} (-5-5x) \\\Leftrightarrow & -6x-3& = &-10-5-5x \\\Leftrightarrow & -6x \color{red}{-3} & = &-15 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -6x+5x& = &-15+3 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-2)& = & -14 \color{red}{-} (9+x) \\\Leftrightarrow & -12x-8& = &-14-9-x \\\Leftrightarrow & -12x \color{red}{-8} & = &-23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -12x+x& = &-23+8 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x+7)& = & 12 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x+14& = &12-5+x \\\Leftrightarrow & -12x \color{red}{+14} & = &7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -12x-x& = &7-14 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-5)& = & 14 \color{red}{+} (-7-5x) \\\Leftrightarrow & -18x-30& = &14-7-5x \\\Leftrightarrow & -18x \color{red}{-30} & = &7 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -18x+5x& = &7+30 \\\Leftrightarrow & -13x& = &37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x-2)& = & 1 \color{red}{+} (8+x) \\\Leftrightarrow & 12x-8& = &1+8+x \\\Leftrightarrow & 12x \color{red}{-8} & = &9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &9+8 \\\Leftrightarrow & 11x& = &17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x-1)& = & -6 \color{red}{+} (4+x) \\\Leftrightarrow & -20x-4& = &-6+4+x \\\Leftrightarrow & -20x \color{red}{-4} & = &-2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -20x-x& = &-2+4 \\\Leftrightarrow & -21x& = &2 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{2}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-4)& = & -3 \color{red}{-} (-4+x) \\\Leftrightarrow & 20x-16& = &-3+4-x \\\Leftrightarrow & 20x \color{red}{-16} & = &1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 20x+x& = &1+16 \\\Leftrightarrow & 21x& = &17 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{17}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{17}{21} & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x+2)& = & 9 \color{red}{-} (8-4x) \\\Leftrightarrow & 5x+10& = &9-8+4x \\\Leftrightarrow & 5x \color{red}{+10} & = &1 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & 5x-4x& = &1-10 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x+4)& = & 12 \color{red}{+} (-8+x) \\\Leftrightarrow & 8x+8& = &12-8+x \\\Leftrightarrow & 8x \color{red}{+8} & = &4 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 8x-x& = &4-8 \\\Leftrightarrow & 7x& = &-4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x+5)& = & -1 \color{red}{+} (-10+x) \\\Leftrightarrow & -25x+25& = &-1-10+x \\\Leftrightarrow & -25x \color{red}{+25} & = &-11 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -25x-x& = &-11-25 \\\Leftrightarrow & -26x& = &-36 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-36}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-6x+6)& = & -14 \color{red}{+} (-4-5x) \\\Leftrightarrow & -36x+36& = &-14-4-5x \\\Leftrightarrow & -36x \color{red}{+36} & = &-18 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -36x+5x& = &-18-36 \\\Leftrightarrow & -31x& = &-54 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-54}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{54}{31} & & \\ & V = \left\{ \frac{54}{31} \right\} & \\\end{align}\)