Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-6)& = & 8 \color{red}{-} (9+4x) \\\Leftrightarrow & 5x-30& = &8-9-4x \\\Leftrightarrow & 5x \color{red}{-30} & = &-1 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & 5x+4x& = &-1+30 \\\Leftrightarrow & 9x& = &29 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{29}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{29}{9} & & \\ & V = \left\{ \frac{29}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x-7)& = & -5 \color{red}{+} (-5+x) \\\Leftrightarrow & 24x-42& = &-5-5+x \\\Leftrightarrow & 24x \color{red}{-42} & = &-10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &-10+42 \\\Leftrightarrow & 23x& = &32 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{32}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x-7)& = & 2 \color{red}{-} (-5-4x) \\\Leftrightarrow & -25x-35& = &2+5+4x \\\Leftrightarrow & -25x \color{red}{-35} & = &7 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-35} \color{blue}{+35} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+35} \\\Leftrightarrow & -25x-4x& = &7+35 \\\Leftrightarrow & -29x& = &42 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{42}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-42}{29} & & \\ & V = \left\{ \frac{-42}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-1)& = & -5 \color{red}{+} (-10+4x) \\\Leftrightarrow & 25x-5& = &-5-10+4x \\\Leftrightarrow & 25x \color{red}{-5} & = &-15 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &-15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & 25x-4x& = &-15+5 \\\Leftrightarrow & 21x& = &-10 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-10}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (2x+3)& = & 11 \color{red}{+} (-15+x) \\\Leftrightarrow & 8x+12& = &11-15+x \\\Leftrightarrow & 8x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &-4-12 \\\Leftrightarrow & 7x& = &-16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x+4)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & 20x+16& = &-4+8-x \\\Leftrightarrow & 20x \color{red}{+16} & = &4 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 20x+x& = &4-16 \\\Leftrightarrow & 21x& = &-12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-4)& = & -3 \color{red}{+} (-12+x) \\\Leftrightarrow & 24x-16& = &-3-12+x \\\Leftrightarrow & 24x \color{red}{-16} & = &-15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 24x-x& = &-15+16 \\\Leftrightarrow & 23x& = &1 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{1}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x-3)& = & -13 \color{red}{+} (10+x) \\\Leftrightarrow & -10x-15& = &-13+10+x \\\Leftrightarrow & -10x \color{red}{-15} & = &-3 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -10x-x& = &-3+15 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x-7)& = & 7 \color{red}{-} (9+x) \\\Leftrightarrow & -4x-14& = &7-9-x \\\Leftrightarrow & -4x \color{red}{-14} & = &-2 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -4x+x& = &-2+14 \\\Leftrightarrow & -3x& = &12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{12}{ \color{red}{-3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+4)& = & 3 \color{red}{+} (-9-3x) \\\Leftrightarrow & 10x+20& = &3-9-3x \\\Leftrightarrow & 10x \color{red}{+20} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 10x+3x& = &-6-20 \\\Leftrightarrow & 13x& = &-26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-26}{ \color{red}{13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x-2)& = & 7 \color{red}{+} (-3+x) \\\Leftrightarrow & -24x-12& = &7-3+x \\\Leftrightarrow & -24x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &4+12 \\\Leftrightarrow & -25x& = &16 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{16}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-16}{25} & & \\ & V = \left\{ \frac{-16}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x-4)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & 2x-8& = &-4+8-x \\\Leftrightarrow & 2x \color{red}{-8} & = &4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 2x+x& = &4+8 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)