Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-1)& = & -14 \color{red}{-} (-12+x) \\\Leftrightarrow & 3x-3& = &-14+12-x \\\Leftrightarrow & 3x \color{red}{-3} & = &-2 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 3x+x& = &-2+3 \\\Leftrightarrow & 4x& = &1 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{1}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x+5)& = & 5 \color{red}{+} (-4+x) \\\Leftrightarrow & 30x+30& = &5-4+x \\\Leftrightarrow & 30x \color{red}{+30} & = &1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &1-30 \\\Leftrightarrow & 29x& = &-29 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-29}{ \color{red}{29} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-4)& = & 7 \color{red}{-} (-3-5x) \\\Leftrightarrow & 36x-24& = &7+3+5x \\\Leftrightarrow & 36x \color{red}{-24} & = &10 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 36x-5x& = &10+24 \\\Leftrightarrow & 31x& = &34 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{34}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{34}{31} & & \\ & V = \left\{ \frac{34}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-1)& = & 12 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-4& = &12+3-x \\\Leftrightarrow & -12x \color{red}{-4} & = &15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &15+4 \\\Leftrightarrow & -11x& = &19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-2)& = & 1 \color{red}{-} (15-2x) \\\Leftrightarrow & -15x-6& = &1-15+2x \\\Leftrightarrow & -15x \color{red}{-6} & = &-14 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -15x-2x& = &-14+6 \\\Leftrightarrow & -17x& = &-8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{8}{17} & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x+5)& = & -11 \color{red}{+} (-9+x) \\\Leftrightarrow & -16x+20& = &-11-9+x \\\Leftrightarrow & -16x \color{red}{+20} & = &-20 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -16x-x& = &-20-20 \\\Leftrightarrow & -17x& = &-40 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-40}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{40}{17} & & \\ & V = \left\{ \frac{40}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-3)& = & 7 \color{red}{-} (-10+4x) \\\Leftrightarrow & -9x-9& = &7+10-4x \\\Leftrightarrow & -9x \color{red}{-9} & = &17 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & -9x+4x& = &17+9 \\\Leftrightarrow & -5x& = &26 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{26}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-26}{5} & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x+4)& = & -10 \color{red}{-} (-15+x) \\\Leftrightarrow & 30x+24& = &-10+15-x \\\Leftrightarrow & 30x \color{red}{+24} & = &5 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 30x+x& = &5-24 \\\Leftrightarrow & 31x& = &-19 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-19}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-19}{31} & & \\ & V = \left\{ \frac{-19}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x+7)& = & -2 \color{red}{-} (1-2x) \\\Leftrightarrow & -15x+21& = &-2-1+2x \\\Leftrightarrow & -15x \color{red}{+21} & = &-3 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &-3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & -15x-2x& = &-3-21 \\\Leftrightarrow & -17x& = &-24 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-24}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{24}{17} & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x+6)& = & -12 \color{red}{+} (6+x) \\\Leftrightarrow & -30x+30& = &-12+6+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-6-30 \\\Leftrightarrow & -31x& = &-36 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-36}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{36}{31} & & \\ & V = \left\{ \frac{36}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+7)& = & -1 \color{red}{-} (-11+3x) \\\Leftrightarrow & -8x+14& = &-1+11-3x \\\Leftrightarrow & -8x \color{red}{+14} & = &10 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -8x+3x& = &10-14 \\\Leftrightarrow & -5x& = &-4 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-4}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+1)& = & -6 \color{red}{+} (6-5x) \\\Leftrightarrow & -18x+6& = &-6+6-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &0 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &0-6 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)