Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x+3)& = & -14 \color{red}{+} (10+x) \\\Leftrightarrow & -24x+12& = &-14+10+x \\\Leftrightarrow & -24x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &-4-12 \\\Leftrightarrow & -25x& = &-16 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-16}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{16}{25} & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-3)& = & 13 \color{red}{-} (-6+4x) \\\Leftrightarrow & 15x-9& = &13+6-4x \\\Leftrightarrow & 15x \color{red}{-9} & = &19 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & 15x+4x& = &19+9 \\\Leftrightarrow & 19x& = &28 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{28}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{28}{19} & & \\ & V = \left\{ \frac{28}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (6x-6)& = & -13 \color{red}{-} (15+x) \\\Leftrightarrow & 24x-24& = &-13-15-x \\\Leftrightarrow & 24x \color{red}{-24} & = &-28 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &-28+24 \\\Leftrightarrow & 25x& = &-4 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-4}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-4}{25} & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-7)& = & 13 \color{red}{-} (8+x) \\\Leftrightarrow & -30x-42& = &13-8-x \\\Leftrightarrow & -30x \color{red}{-42} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -30x+x& = &5+42 \\\Leftrightarrow & -29x& = &47 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{47}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-47}{29} & & \\ & V = \left\{ \frac{-47}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-2)& = & -11 \color{red}{-} (-9+x) \\\Leftrightarrow & 16x-8& = &-11+9-x \\\Leftrightarrow & 16x \color{red}{-8} & = &-2 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 16x+x& = &-2+8 \\\Leftrightarrow & 17x& = &6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x+2)& = & -10 \color{red}{+} (4+x) \\\Leftrightarrow & -6x+4& = &-10+4+x \\\Leftrightarrow & -6x \color{red}{+4} & = &-6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -6x-x& = &-6-4 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x-1)& = & -9 \color{red}{-} (2+2x) \\\Leftrightarrow & 15x-5& = &-9-2-2x \\\Leftrightarrow & 15x \color{red}{-5} & = &-11 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 15x+2x& = &-11+5 \\\Leftrightarrow & 17x& = &-6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+2)& = & 7 \color{red}{-} (-3+x) \\\Leftrightarrow & 20x+8& = &7+3-x \\\Leftrightarrow & 20x \color{red}{+8} & = &10 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &10-8 \\\Leftrightarrow & 21x& = &2 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{2}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+3)& = & -10 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+18& = &-10+10-x \\\Leftrightarrow & -12x \color{red}{+18} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &0-18 \\\Leftrightarrow & -11x& = &-18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x+3)& = & -13 \color{red}{+} (6+x) \\\Leftrightarrow & 6x+9& = &-13+6+x \\\Leftrightarrow & 6x \color{red}{+9} & = &-7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 6x-x& = &-7-9 \\\Leftrightarrow & 5x& = &-16 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-16}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-16}{5} & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x+2)& = & -11 \color{red}{+} (-10-2x) \\\Leftrightarrow & 5x+10& = &-11-10-2x \\\Leftrightarrow & 5x \color{red}{+10} & = &-21 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &-21 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 5x+2x& = &-21-10 \\\Leftrightarrow & 7x& = &-31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+5)& = & 9 \color{red}{+} (4+x) \\\Leftrightarrow & -18x+30& = &9+4+x \\\Leftrightarrow & -18x \color{red}{+30} & = &13 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -18x-x& = &13-30 \\\Leftrightarrow & -19x& = &-17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)