Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x+2)& = & -1 \color{red}{+} (11+x) \\\Leftrightarrow & -5x+10& = &-1+11+x \\\Leftrightarrow & -5x \color{red}{+10} & = &10 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -5x-x& = &10-10 \\\Leftrightarrow & -6x& = &0 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{0}{ \color{red}{-6} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x-7)& = & 5 \color{red}{-} (12+x) \\\Leftrightarrow & 24x-42& = &5-12-x \\\Leftrightarrow & 24x \color{red}{-42} & = &-7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 24x+x& = &-7+42 \\\Leftrightarrow & 25x& = &35 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{35}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x+1)& = & -8 \color{red}{+} (-11+x) \\\Leftrightarrow & 20x+5& = &-8-11+x \\\Leftrightarrow & 20x \color{red}{+5} & = &-19 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 20x-x& = &-19-5 \\\Leftrightarrow & 19x& = &-24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-4)& = & 7 \color{red}{-} (8+x) \\\Leftrightarrow & -6x-24& = &7-8-x \\\Leftrightarrow & -6x \color{red}{-24} & = &-1 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -6x+x& = &-1+24 \\\Leftrightarrow & -5x& = &23 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{23}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-7)& = & -4 \color{red}{-} (4+3x) \\\Leftrightarrow & 8x-14& = &-4-4-3x \\\Leftrightarrow & 8x \color{red}{-14} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 8x+3x& = &-8+14 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-7)& = & -9 \color{red}{+} (-1+x) \\\Leftrightarrow & 18x-21& = &-9-1+x \\\Leftrightarrow & 18x \color{red}{-21} & = &-10 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 18x-x& = &-10+21 \\\Leftrightarrow & 17x& = &11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x+6)& = & -3 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x+12& = &-3-1+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-4-12 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x+7)& = & -14 \color{red}{-} (-12+x) \\\Leftrightarrow & 30x+42& = &-14+12-x \\\Leftrightarrow & 30x \color{red}{+42} & = &-2 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 30x+x& = &-2-42 \\\Leftrightarrow & 31x& = &-44 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-44}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-44}{31} & & \\ & V = \left\{ \frac{-44}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x-6)& = & 11 \color{red}{-} (-12-5x) \\\Leftrightarrow & 16x-24& = &11+12+5x \\\Leftrightarrow & 16x \color{red}{-24} & = &23 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &23 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 16x-5x& = &23+24 \\\Leftrightarrow & 11x& = &47 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{47}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{47}{11} & & \\ & V = \left\{ \frac{47}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x+4)& = & 7 \color{red}{+} (5+x) \\\Leftrightarrow & 2x+8& = &7+5+x \\\Leftrightarrow & 2x \color{red}{+8} & = &12 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 2x-x& = &12-8 \\\Leftrightarrow & x& = &4 \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-1)& = & 5 \color{red}{+} (-15+x) \\\Leftrightarrow & 20x-4& = &5-15+x \\\Leftrightarrow & 20x \color{red}{-4} & = &-10 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 20x-x& = &-10+4 \\\Leftrightarrow & 19x& = &-6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x+3)& = & 10 \color{red}{+} (-15-2x) \\\Leftrightarrow & 3x+9& = &10-15-2x \\\Leftrightarrow & 3x \color{red}{+9} & = &-5 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & 3x+2x& = &-5-9 \\\Leftrightarrow & 5x& = &-14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)