Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x-7)& = & 13 \color{red}{+} (-7+x) \\\Leftrightarrow & -25x-35& = &13-7+x \\\Leftrightarrow & -25x \color{red}{-35} & = &6 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -25x-x& = &6+35 \\\Leftrightarrow & -26x& = &41 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{41}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-41}{26} & & \\ & V = \left\{ \frac{-41}{26} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+6)& = & -11 \color{red}{-} (5+3x) \\\Leftrightarrow & -10x+30& = &-11-5-3x \\\Leftrightarrow & -10x \color{red}{+30} & = &-16 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & -10x+3x& = &-16-30 \\\Leftrightarrow & -7x& = &-46 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-46}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{46}{7} & & \\ & V = \left\{ \frac{46}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x+2)& = & 7 \color{red}{-} (-12+3x) \\\Leftrightarrow & -4x+8& = &7+12-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &19 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &19-8 \\\Leftrightarrow & -x& = &11 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{11}{ \color{red}{-1} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-2x-2)& = & -9 \color{red}{-} (7-3x) \\\Leftrightarrow & -10x-10& = &-9-7+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &-16 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &-16+10 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x+7)& = & -13 \color{red}{+} (-6-4x) \\\Leftrightarrow & 9x+21& = &-13-6-4x \\\Leftrightarrow & 9x \color{red}{+21} & = &-19 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 9x+4x& = &-19-21 \\\Leftrightarrow & 13x& = &-40 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-40}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-40}{13} & & \\ & V = \left\{ \frac{-40}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-4)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & 24x-16& = &-10-3-x \\\Leftrightarrow & 24x \color{red}{-16} & = &-13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 24x+x& = &-13+16 \\\Leftrightarrow & 25x& = &3 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{3}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{3}{25} & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-4)& = & -9 \color{red}{-} (6+x) \\\Leftrightarrow & 6x-24& = &-9-6-x \\\Leftrightarrow & 6x \color{red}{-24} & = &-15 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 6x+x& = &-15+24 \\\Leftrightarrow & 7x& = &9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x-5)& = & -12 \color{red}{-} (5+x) \\\Leftrightarrow & -12x-10& = &-12-5-x \\\Leftrightarrow & -12x \color{red}{-10} & = &-17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -12x+x& = &-17+10 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x-1)& = & 13 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-4& = &13-3+x \\\Leftrightarrow & -12x \color{red}{-4} & = &10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &10+4 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-4)& = & 9 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x-12& = &9+15-x \\\Leftrightarrow & 12x \color{red}{-12} & = &24 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &24+12 \\\Leftrightarrow & 13x& = &36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{36}{13} & & \\ & V = \left\{ \frac{36}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-1)& = & -15 \color{red}{-} (-6+x) \\\Leftrightarrow & -12x-6& = &-15+6-x \\\Leftrightarrow & -12x \color{red}{-6} & = &-9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &-9+6 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+7)& = & -5 \color{red}{+} (-12-3x) \\\Leftrightarrow & 25x+35& = &-5-12-3x \\\Leftrightarrow & 25x \color{red}{+35} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 25x+3x& = &-17-35 \\\Leftrightarrow & 28x& = &-52 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-52}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)