Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+2)& = & -3 \color{red}{-} (-1+x) \\\Leftrightarrow & 20x+10& = &-3+1-x \\\Leftrightarrow & 20x \color{red}{+10} & = &-2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 20x+x& = &-2-10 \\\Leftrightarrow & 21x& = &-12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x+7)& = & -2 \color{red}{+} (1+x) \\\Leftrightarrow & 36x+42& = &-2+1+x \\\Leftrightarrow & 36x \color{red}{+42} & = &-1 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 36x-x& = &-1-42 \\\Leftrightarrow & 35x& = &-43 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-43}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-43}{35} & & \\ & V = \left\{ \frac{-43}{35} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-5)& = & -8 \color{red}{+} (-2+x) \\\Leftrightarrow & -18x-30& = &-8-2+x \\\Leftrightarrow & -18x \color{red}{-30} & = &-10 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -18x-x& = &-10+30 \\\Leftrightarrow & -19x& = &20 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{20}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-20}{19} & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x-3)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & -18x-18& = &6-11+x \\\Leftrightarrow & -18x \color{red}{-18} & = &-5 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -18x-x& = &-5+18 \\\Leftrightarrow & -19x& = &13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x-2)& = & 1 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-12& = &1+3-x \\\Leftrightarrow & -12x \color{red}{-12} & = &4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &4+12 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-2)& = & -8 \color{red}{-} (-12+x) \\\Leftrightarrow & 4x-8& = &-8+12-x \\\Leftrightarrow & 4x \color{red}{-8} & = &4 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 4x+x& = &4+8 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x+4)& = & -2 \color{red}{-} (-10+3x) \\\Leftrightarrow & -20x+16& = &-2+10-3x \\\Leftrightarrow & -20x \color{red}{+16} & = &8 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & -20x+3x& = &8-16 \\\Leftrightarrow & -17x& = &-8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{8}{17} & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x+6)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & -36x+36& = &-15+6+x \\\Leftrightarrow & -36x \color{red}{+36} & = &-9 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -36x-x& = &-9-36 \\\Leftrightarrow & -37x& = &-45 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-45}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{45}{37} & & \\ & V = \left\{ \frac{45}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x+1)& = & 2 \color{red}{-} (-5+x) \\\Leftrightarrow & 15x+5& = &2+5-x \\\Leftrightarrow & 15x \color{red}{+5} & = &7 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 15x+x& = &7-5 \\\Leftrightarrow & 16x& = &2 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{2}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-4)& = & -13 \color{red}{-} (-7+x) \\\Leftrightarrow & -15x-12& = &-13+7-x \\\Leftrightarrow & -15x \color{red}{-12} & = &-6 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -15x+x& = &-6+12 \\\Leftrightarrow & -14x& = &6 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{6}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-3)& = & 11 \color{red}{-} (-9+x) \\\Leftrightarrow & 18x-9& = &11+9-x \\\Leftrightarrow & 18x \color{red}{-9} & = &20 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 18x+x& = &20+9 \\\Leftrightarrow & 19x& = &29 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{29}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{29}{19} & & \\ & V = \left\{ \frac{29}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x-5)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x-15& = &-5-6+x \\\Leftrightarrow & 6x \color{red}{-15} & = &-11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 6x-x& = &-11+15 \\\Leftrightarrow & 5x& = &4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)