Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-2)& = & -9 \color{red}{+} (9+x) \\\Leftrightarrow & 30x-12& = &-9+9+x \\\Leftrightarrow & 30x \color{red}{-12} & = &0 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 30x-x& = &0+12 \\\Leftrightarrow & 29x& = &12 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{12}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{12}{29} & & \\ & V = \left\{ \frac{12}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x+1)& = & -15 \color{red}{-} (-11-2x) \\\Leftrightarrow & -3x+3& = &-15+11+2x \\\Leftrightarrow & -3x \color{red}{+3} & = &-4 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -3x-2x& = &-4-3 \\\Leftrightarrow & -5x& = &-7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-1)& = & -12 \color{red}{-} (-3-5x) \\\Leftrightarrow & 18x-6& = &-12+3+5x \\\Leftrightarrow & 18x \color{red}{-6} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 18x-5x& = &-9+6 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-2)& = & -12 \color{red}{+} (6-5x) \\\Leftrightarrow & 6x-6& = &-12+6-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &-6+6 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x+4)& = & -6 \color{red}{+} (9+x) \\\Leftrightarrow & 24x+16& = &-6+9+x \\\Leftrightarrow & 24x \color{red}{+16} & = &3 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 24x-x& = &3-16 \\\Leftrightarrow & 23x& = &-13 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-13}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+7)& = & 1 \color{red}{-} (-2-2x) \\\Leftrightarrow & 15x+35& = &1+2+2x \\\Leftrightarrow & 15x \color{red}{+35} & = &3 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 15x-2x& = &3-35 \\\Leftrightarrow & 13x& = &-32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-32}{13} & & \\ & V = \left\{ \frac{-32}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x+6)& = & 3 \color{red}{+} (1-5x) \\\Leftrightarrow & -18x+18& = &3+1-5x \\\Leftrightarrow & -18x \color{red}{+18} & = &4 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -18x+5x& = &4-18 \\\Leftrightarrow & -13x& = &-14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x+1)& = & 15 \color{red}{-} (6+x) \\\Leftrightarrow & -30x+6& = &15-6-x \\\Leftrightarrow & -30x \color{red}{+6} & = &9 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -30x+x& = &9-6 \\\Leftrightarrow & -29x& = &3 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{3}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x-6)& = & -13 \color{red}{-} (9+x) \\\Leftrightarrow & -8x-12& = &-13-9-x \\\Leftrightarrow & -8x \color{red}{-12} & = &-22 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -8x+x& = &-22+12 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x-4)& = & 9 \color{red}{+} (-4+4x) \\\Leftrightarrow & 5x-20& = &9-4+4x \\\Leftrightarrow & 5x \color{red}{-20} & = &5 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & 5x-4x& = &5+20 \\\Leftrightarrow & x& = &25 \\ & V = \left\{ 25 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x-1)& = & 1 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x-3& = &1+1-x \\\Leftrightarrow & -12x \color{red}{-3} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -12x+x& = &2+3 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x-4)& = & 3 \color{red}{+} (12+x) \\\Leftrightarrow & 20x-20& = &3+12+x \\\Leftrightarrow & 20x \color{red}{-20} & = &15 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &15+20 \\\Leftrightarrow & 19x& = &35 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{35}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)