Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+2)& = & 12 \color{red}{-} (4+x) \\\Leftrightarrow & 15x+6& = &12-4-x \\\Leftrightarrow & 15x \color{red}{+6} & = &8 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 15x+x& = &8-6 \\\Leftrightarrow & 16x& = &2 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{2}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x+6)& = & 1 \color{red}{-} (7+3x) \\\Leftrightarrow & 20x+30& = &1-7-3x \\\Leftrightarrow & 20x \color{red}{+30} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & 20x+3x& = &-6-30 \\\Leftrightarrow & 23x& = &-36 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-36}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-36}{23} & & \\ & V = \left\{ \frac{-36}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+7)& = & -15 \color{red}{-} (-3-3x) \\\Leftrightarrow & 4x+14& = &-15+3+3x \\\Leftrightarrow & 4x \color{red}{+14} & = &-12 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 4x-3x& = &-12-14 \\\Leftrightarrow & x& = &-26 \\ & V = \left\{ -26 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x-4)& = & -5 \color{red}{-} (12-5x) \\\Leftrightarrow & -6x-12& = &-5-12+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &-17 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &-17+12 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-4)& = & 1 \color{red}{+} (-4-3x) \\\Leftrightarrow & 4x-16& = &1-4-3x \\\Leftrightarrow & 4x \color{red}{-16} & = &-3 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 4x+3x& = &-3+16 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x-1)& = & -4 \color{red}{-} (1+x) \\\Leftrightarrow & -16x-4& = &-4-1-x \\\Leftrightarrow & -16x \color{red}{-4} & = &-5 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -16x+x& = &-5+4 \\\Leftrightarrow & -15x& = &-1 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-1}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x+2)& = & 2 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x+4& = &2+4-x \\\Leftrightarrow & 12x \color{red}{+4} & = &6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &6-4 \\\Leftrightarrow & 13x& = &2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+5)& = & 15 \color{red}{-} (13-3x) \\\Leftrightarrow & 16x+20& = &15-13+3x \\\Leftrightarrow & 16x \color{red}{+20} & = &2 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & 16x-3x& = &2-20 \\\Leftrightarrow & 13x& = &-18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x+2)& = & 3 \color{red}{-} (12+x) \\\Leftrightarrow & 18x+6& = &3-12-x \\\Leftrightarrow & 18x \color{red}{+6} & = &-9 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &-9-6 \\\Leftrightarrow & 19x& = &-15 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-15}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-15}{19} & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x-7)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & -6x-14& = &6-11+x \\\Leftrightarrow & -6x \color{red}{-14} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -6x-x& = &-5+14 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x+6)& = & -13 \color{red}{-} (-6+x) \\\Leftrightarrow & 16x+24& = &-13+6-x \\\Leftrightarrow & 16x \color{red}{+24} & = &-7 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 16x+x& = &-7-24 \\\Leftrightarrow & 17x& = &-31 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-31}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-31}{17} & & \\ & V = \left\{ \frac{-31}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+6)& = & -9 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x+36& = &-9+2-x \\\Leftrightarrow & 12x \color{red}{+36} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 12x+x& = &-7-36 \\\Leftrightarrow & 13x& = &-43 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-43}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-43}{13} & & \\ & V = \left\{ \frac{-43}{13} \right\} & \\\end{align}\)