Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x-7)& = & -12 \color{red}{-} (5-5x) \\\Leftrightarrow & 36x-42& = &-12-5+5x \\\Leftrightarrow & 36x \color{red}{-42} & = &-17 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 36x-5x& = &-17+42 \\\Leftrightarrow & 31x& = &25 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{25}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{25}{31} & & \\ & V = \left\{ \frac{25}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+2)& = & -8 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+4& = &-8-6-x \\\Leftrightarrow & -6x \color{red}{+4} & = &-14 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -6x+x& = &-14-4 \\\Leftrightarrow & -5x& = &-18 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-18}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x+1)& = & -15 \color{red}{-} (-4+x) \\\Leftrightarrow & -2x+2& = &-15+4-x \\\Leftrightarrow & -2x \color{red}{+2} & = &-11 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -2x+x& = &-11-2 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-4)& = & -7 \color{red}{+} (1+x) \\\Leftrightarrow & 6x-12& = &-7+1+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-6+12 \\\Leftrightarrow & 5x& = &6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-5)& = & -14 \color{red}{-} (-10-2x) \\\Leftrightarrow & 15x-25& = &-14+10+2x \\\Leftrightarrow & 15x \color{red}{-25} & = &-4 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & 15x-2x& = &-4+25 \\\Leftrightarrow & 13x& = &21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-4)& = & -11 \color{red}{+} (-13+3x) \\\Leftrightarrow & -25x-20& = &-11-13+3x \\\Leftrightarrow & -25x \color{red}{-20} & = &-24 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -25x-3x& = &-24+20 \\\Leftrightarrow & -28x& = &-4 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-4}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x+2)& = & 12 \color{red}{+} (11-4x) \\\Leftrightarrow & 25x+10& = &12+11-4x \\\Leftrightarrow & 25x \color{red}{+10} & = &23 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &23 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & 25x+4x& = &23-10 \\\Leftrightarrow & 29x& = &13 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{13}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{13}{29} & & \\ & V = \left\{ \frac{13}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x-3)& = & -10 \color{red}{+} (-9-2x) \\\Leftrightarrow & 5x-15& = &-10-9-2x \\\Leftrightarrow & 5x \color{red}{-15} & = &-19 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 5x+2x& = &-19+15 \\\Leftrightarrow & 7x& = &-4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x-2)& = & 4 \color{red}{-} (1-2x) \\\Leftrightarrow & 15x-10& = &4-1+2x \\\Leftrightarrow & 15x \color{red}{-10} & = &3 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+10} \\\Leftrightarrow & 15x-2x& = &3+10 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-1)& = & 11 \color{red}{+} (15+x) \\\Leftrightarrow & -10x-2& = &11+15+x \\\Leftrightarrow & -10x \color{red}{-2} & = &26 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -10x-x& = &26+2 \\\Leftrightarrow & -11x& = &28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+5)& = & 4 \color{red}{-} (8-3x) \\\Leftrightarrow & 10x+10& = &4-8+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-4 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &-4-10 \\\Leftrightarrow & 7x& = &-14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-14}{ \color{red}{7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x-6)& = & -9 \color{red}{-} (-2+x) \\\Leftrightarrow & -20x-24& = &-9+2-x \\\Leftrightarrow & -20x \color{red}{-24} & = &-7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -20x+x& = &-7+24 \\\Leftrightarrow & -19x& = &17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)