Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-3)& = & 9 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-18& = &9-7-x \\\Leftrightarrow & -12x \color{red}{-18} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &2+18 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x-5)& = & 8 \color{red}{-} (14-5x) \\\Leftrightarrow & 16x-20& = &8-14+5x \\\Leftrightarrow & 16x \color{red}{-20} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+20} \\\Leftrightarrow & 16x-5x& = &-6+20 \\\Leftrightarrow & 11x& = &14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x+5)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x+30& = &-2+14-x \\\Leftrightarrow & -12x \color{red}{+30} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -12x+x& = &12-30 \\\Leftrightarrow & -11x& = &-18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x-3)& = & -4 \color{red}{+} (-9+x) \\\Leftrightarrow & -30x-15& = &-4-9+x \\\Leftrightarrow & -30x \color{red}{-15} & = &-13 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &-13+15 \\\Leftrightarrow & -31x& = &2 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{2}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-2}{31} & & \\ & V = \left\{ \frac{-2}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-7)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & -24x-42& = &6-7+x \\\Leftrightarrow & -24x \color{red}{-42} & = &-1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &-1+42 \\\Leftrightarrow & -25x& = &41 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{41}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-41}{25} & & \\ & V = \left\{ \frac{-41}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x+6)& = & -11 \color{red}{+} (1+x) \\\Leftrightarrow & 12x+12& = &-11+1+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-10-12 \\\Leftrightarrow & 11x& = &-22 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-22}{ \color{red}{11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+5)& = & 5 \color{red}{-} (-6-4x) \\\Leftrightarrow & -5x+25& = &5+6+4x \\\Leftrightarrow & -5x \color{red}{+25} & = &11 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & -5x-4x& = &11-25 \\\Leftrightarrow & -9x& = &-14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-7)& = & 12 \color{red}{+} (10+x) \\\Leftrightarrow & -36x-42& = &12+10+x \\\Leftrightarrow & -36x \color{red}{-42} & = &22 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -36x-x& = &22+42 \\\Leftrightarrow & -37x& = &64 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{64}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-64}{37} & & \\ & V = \left\{ \frac{-64}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x-6)& = & -5 \color{red}{+} (10-5x) \\\Leftrightarrow & 36x-36& = &-5+10-5x \\\Leftrightarrow & 36x \color{red}{-36} & = &5 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & 36x+5x& = &5+36 \\\Leftrightarrow & 41x& = &41 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{41}{ \color{red}{41} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x-6)& = & 1 \color{red}{-} (-10+2x) \\\Leftrightarrow & 9x-18& = &1+10-2x \\\Leftrightarrow & 9x \color{red}{-18} & = &11 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 9x+2x& = &11+18 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-1)& = & -9 \color{red}{+} (-9+x) \\\Leftrightarrow & -24x-4& = &-9-9+x \\\Leftrightarrow & -24x \color{red}{-4} & = &-18 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -24x-x& = &-18+4 \\\Leftrightarrow & -25x& = &-14 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-14}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x-5)& = & 10 \color{red}{-} (-9+x) \\\Leftrightarrow & -8x-20& = &10+9-x \\\Leftrightarrow & -8x \color{red}{-20} & = &19 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -8x+x& = &19+20 \\\Leftrightarrow & -7x& = &39 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{39}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-39}{7} & & \\ & V = \left\{ \frac{-39}{7} \right\} & \\\end{align}\)