Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x-7)& = & -13 \color{red}{-} (5-5x) \\\Leftrightarrow & 6x-42& = &-13-5+5x \\\Leftrightarrow & 6x \color{red}{-42} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 6x-5x& = &-18+42 \\\Leftrightarrow & x& = &24 \\ & V = \left\{ 24 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+7)& = & -3 \color{red}{+} (14-4x) \\\Leftrightarrow & -5x+35& = &-3+14-4x \\\Leftrightarrow & -5x \color{red}{+35} & = &11 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & -5x+4x& = &11-35 \\\Leftrightarrow & -x& = &-24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-24}{ \color{red}{-1} } \\\Leftrightarrow & x = 24 & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x+1)& = & 10 \color{red}{+} (4+2x) \\\Leftrightarrow & 3x+3& = &10+4+2x \\\Leftrightarrow & 3x \color{red}{+3} & = &14 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & 3x-2x& = &14-3 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+1)& = & 7 \color{red}{-} (15+x) \\\Leftrightarrow & -12x+3& = &7-15-x \\\Leftrightarrow & -12x \color{red}{+3} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -12x+x& = &-8-3 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-6)& = & -9 \color{red}{-} (-12-5x) \\\Leftrightarrow & 18x-18& = &-9+12+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &3 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &3+18 \\\Leftrightarrow & 13x& = &21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x+5)& = & -11 \color{red}{+} (3+x) \\\Leftrightarrow & -30x+30& = &-11+3+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-8 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-8-30 \\\Leftrightarrow & -31x& = &-38 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-38}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{38}{31} & & \\ & V = \left\{ \frac{38}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+2)& = & -13 \color{red}{-} (-6+x) \\\Leftrightarrow & 30x+10& = &-13+6-x \\\Leftrightarrow & 30x \color{red}{+10} & = &-7 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 30x+x& = &-7-10 \\\Leftrightarrow & 31x& = &-17 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-17}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-17}{31} & & \\ & V = \left\{ \frac{-17}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (6x-6)& = & -4 \color{red}{+} (-6-5x) \\\Leftrightarrow & 36x-36& = &-4-6-5x \\\Leftrightarrow & 36x \color{red}{-36} & = &-10 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & 36x+5x& = &-10+36 \\\Leftrightarrow & 41x& = &26 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{26}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{26}{41} & & \\ & V = \left\{ \frac{26}{41} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+3)& = & 1 \color{red}{+} (-12-2x) \\\Leftrightarrow & 3x+9& = &1-12-2x \\\Leftrightarrow & 3x \color{red}{+9} & = &-11 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & 3x+2x& = &-11-9 \\\Leftrightarrow & 5x& = &-20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-20}{ \color{red}{5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-5)& = & 13 \color{red}{-} (-6-5x) \\\Leftrightarrow & -8x-10& = &13+6+5x \\\Leftrightarrow & -8x \color{red}{-10} & = &19 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+10} \\\Leftrightarrow & -8x-5x& = &19+10 \\\Leftrightarrow & -13x& = &29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+5)& = & -3 \color{red}{-} (9-4x) \\\Leftrightarrow & 9x+15& = &-3-9+4x \\\Leftrightarrow & 9x \color{red}{+15} & = &-12 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &-12 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 9x-4x& = &-12-15 \\\Leftrightarrow & 5x& = &-27 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-27}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-27}{5} & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-4)& = & 7 \color{red}{+} (8+x) \\\Leftrightarrow & 24x-24& = &7+8+x \\\Leftrightarrow & 24x \color{red}{-24} & = &15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &15+24 \\\Leftrightarrow & 23x& = &39 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{39}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{39}{23} & & \\ & V = \left\{ \frac{39}{23} \right\} & \\\end{align}\)