Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x+3)& = & -13 \color{red}{+} (5-5x) \\\Leftrightarrow & 6x+6& = &-13+5-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-8 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &-8-6 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x+6)& = & 8 \color{red}{+} (-13+x) \\\Leftrightarrow & -30x+36& = &8-13+x \\\Leftrightarrow & -30x \color{red}{+36} & = &-5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -30x-x& = &-5-36 \\\Leftrightarrow & -31x& = &-41 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-41}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{41}{31} & & \\ & V = \left\{ \frac{41}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+1)& = & 15 \color{red}{-} (8-5x) \\\Leftrightarrow & 16x+4& = &15-8+5x \\\Leftrightarrow & 16x \color{red}{+4} & = &7 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 16x-5x& = &7-4 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x+1)& = & -7 \color{red}{-} (-10-2x) \\\Leftrightarrow & 25x+5& = &-7+10+2x \\\Leftrightarrow & 25x \color{red}{+5} & = &3 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 25x-2x& = &3-5 \\\Leftrightarrow & 23x& = &-2 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-2}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x+4)& = & -6 \color{red}{-} (6+x) \\\Leftrightarrow & 30x+24& = &-6-6-x \\\Leftrightarrow & 30x \color{red}{+24} & = &-12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 30x+x& = &-12-24 \\\Leftrightarrow & 31x& = &-36 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-36}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-36}{31} & & \\ & V = \left\{ \frac{-36}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x-3)& = & -6 \color{red}{-} (-5-5x) \\\Leftrightarrow & -8x-12& = &-6+5+5x \\\Leftrightarrow & -8x \color{red}{-12} & = &-1 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -8x-5x& = &-1+12 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+7)& = & 6 \color{red}{-} (3+x) \\\Leftrightarrow & -12x+42& = &6-3-x \\\Leftrightarrow & -12x \color{red}{+42} & = &3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &3-42 \\\Leftrightarrow & -11x& = &-39 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-39}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{39}{11} & & \\ & V = \left\{ \frac{39}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x-7)& = & -11 \color{red}{-} (-7-5x) \\\Leftrightarrow & -16x-28& = &-11+7+5x \\\Leftrightarrow & -16x \color{red}{-28} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & -16x-5x& = &-4+28 \\\Leftrightarrow & -21x& = &24 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{24}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+7)& = & 2 \color{red}{+} (13+x) \\\Leftrightarrow & 30x+42& = &2+13+x \\\Leftrightarrow & 30x \color{red}{+42} & = &15 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &15-42 \\\Leftrightarrow & 29x& = &-27 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-27}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-27}{29} & & \\ & V = \left\{ \frac{-27}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-6)& = & 4 \color{red}{+} (14-2x) \\\Leftrightarrow & -25x-30& = &4+14-2x \\\Leftrightarrow & -25x \color{red}{-30} & = &18 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & -25x+2x& = &18+30 \\\Leftrightarrow & -23x& = &48 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{48}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-48}{23} & & \\ & V = \left\{ \frac{-48}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+5)& = & 6 \color{red}{-} (11+3x) \\\Leftrightarrow & -4x+10& = &6-11-3x \\\Leftrightarrow & -4x \color{red}{+10} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -4x+3x& = &-5-10 \\\Leftrightarrow & -x& = &-15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-15}{ \color{red}{-1} } \\\Leftrightarrow & x = 15 & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-3)& = & 2 \color{red}{+} (7+2x) \\\Leftrightarrow & -5x-15& = &2+7+2x \\\Leftrightarrow & -5x \color{red}{-15} & = &9 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -5x-2x& = &9+15 \\\Leftrightarrow & -7x& = &24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)