Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+5)& = & -5 \color{red}{+} (13+x) \\\Leftrightarrow & 12x+10& = &-5+13+x \\\Leftrightarrow & 12x \color{red}{+10} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 12x-x& = &8-10 \\\Leftrightarrow & 11x& = &-2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x+7)& = & 11 \color{red}{+} (-4-5x) \\\Leftrightarrow & -6x+42& = &11-4-5x \\\Leftrightarrow & -6x \color{red}{+42} & = &7 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -6x+5x& = &7-42 \\\Leftrightarrow & -x& = &-35 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-35}{ \color{red}{-1} } \\\Leftrightarrow & x = 35 & & \\ & V = \left\{ 35 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x-2)& = & -2 \color{red}{+} (-14+x) \\\Leftrightarrow & -30x-10& = &-2-14+x \\\Leftrightarrow & -30x \color{red}{-10} & = &-16 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -30x-x& = &-16+10 \\\Leftrightarrow & -31x& = &-6 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-6}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-2)& = & 15 \color{red}{+} (-14-5x) \\\Leftrightarrow & -6x-4& = &15-14-5x \\\Leftrightarrow & -6x \color{red}{-4} & = &1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & -6x+5x& = &1+4 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x+5)& = & -8 \color{red}{-} (8+3x) \\\Leftrightarrow & -8x+20& = &-8-8-3x \\\Leftrightarrow & -8x \color{red}{+20} & = &-16 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -8x+3x& = &-16-20 \\\Leftrightarrow & -5x& = &-36 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-36}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{36}{5} & & \\ & V = \left\{ \frac{36}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x-5)& = & 10 \color{red}{+} (-15+3x) \\\Leftrightarrow & -8x-10& = &10-15+3x \\\Leftrightarrow & -8x \color{red}{-10} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -8x-3x& = &-5+10 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+7)& = & 15 \color{red}{-} (-13-5x) \\\Leftrightarrow & 8x+14& = &15+13+5x \\\Leftrightarrow & 8x \color{red}{+14} & = &28 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &28 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & 8x-5x& = &28-14 \\\Leftrightarrow & 3x& = &14 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{14}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{14}{3} & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x-2)& = & -5 \color{red}{+} (10+4x) \\\Leftrightarrow & 9x-6& = &-5+10+4x \\\Leftrightarrow & 9x \color{red}{-6} & = &5 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & 9x-4x& = &5+6 \\\Leftrightarrow & 5x& = &11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+1)& = & 12 \color{red}{+} (5+x) \\\Leftrightarrow & 15x+3& = &12+5+x \\\Leftrightarrow & 15x \color{red}{+3} & = &17 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 15x-x& = &17-3 \\\Leftrightarrow & 14x& = &14 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{14}{ \color{red}{14} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-5x-5)& = & -10 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x-30& = &-10+9-x \\\Leftrightarrow & -30x \color{red}{-30} & = &-1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -30x+x& = &-1+30 \\\Leftrightarrow & -29x& = &29 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{29}{ \color{red}{-29} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-4)& = & -1 \color{red}{-} (9-4x) \\\Leftrightarrow & 5x-20& = &-1-9+4x \\\Leftrightarrow & 5x \color{red}{-20} & = &-10 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &-10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & 5x-4x& = &-10+20 \\\Leftrightarrow & x& = &10 \\ & V = \left\{ 10 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x-7)& = & 1 \color{red}{-} (-11+x) \\\Leftrightarrow & -18x-42& = &1+11-x \\\Leftrightarrow & -18x \color{red}{-42} & = &12 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -18x+x& = &12+42 \\\Leftrightarrow & -17x& = &54 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{54}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-54}{17} & & \\ & V = \left\{ \frac{-54}{17} \right\} & \\\end{align}\)