Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x+2)& = & -15 \color{red}{-} (-4-5x) \\\Leftrightarrow & 6x+6& = &-15+4+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &-11-6 \\\Leftrightarrow & x& = &-17 \\ & V = \left\{ -17 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+4)& = & 8 \color{red}{-} (15+3x) \\\Leftrightarrow & 10x+8& = &8-15-3x \\\Leftrightarrow & 10x \color{red}{+8} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 10x+3x& = &-7-8 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+1)& = & -13 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x+3& = &-13+9-x \\\Leftrightarrow & 12x \color{red}{+3} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &-4-3 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x-3)& = & -12 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-6& = &-12+5+x \\\Leftrightarrow & -12x \color{red}{-6} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &-7+6 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x+6)& = & -7 \color{red}{+} (11-3x) \\\Leftrightarrow & 4x+12& = &-7+11-3x \\\Leftrightarrow & 4x \color{red}{+12} & = &4 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 4x+3x& = &4-12 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x-5)& = & 9 \color{red}{-} (11+3x) \\\Leftrightarrow & 10x-10& = &9-11-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &-2+10 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-7)& = & 9 \color{red}{-} (3+2x) \\\Leftrightarrow & -9x-21& = &9-3-2x \\\Leftrightarrow & -9x \color{red}{-21} & = &6 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & -9x+2x& = &6+21 \\\Leftrightarrow & -7x& = &27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x-3)& = & -2 \color{red}{+} (-3-4x) \\\Leftrightarrow & 25x-15& = &-2-3-4x \\\Leftrightarrow & 25x \color{red}{-15} & = &-5 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 25x+4x& = &-5+15 \\\Leftrightarrow & 29x& = &10 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{10}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{10}{29} & & \\ & V = \left\{ \frac{10}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+2)& = & -15 \color{red}{-} (7-5x) \\\Leftrightarrow & 16x+8& = &-15-7+5x \\\Leftrightarrow & 16x \color{red}{+8} & = &-22 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &-22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & 16x-5x& = &-22-8 \\\Leftrightarrow & 11x& = &-30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x+3)& = & 14 \color{red}{+} (5+x) \\\Leftrightarrow & 12x+12& = &14+5+x \\\Leftrightarrow & 12x \color{red}{+12} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &19-12 \\\Leftrightarrow & 11x& = &7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x-6)& = & -4 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x-36& = &-4+10-x \\\Leftrightarrow & -24x \color{red}{-36} & = &6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -24x+x& = &6+36 \\\Leftrightarrow & -23x& = &42 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{42}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-42}{23} & & \\ & V = \left\{ \frac{-42}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+4)& = & 10 \color{red}{-} (-7+x) \\\Leftrightarrow & 6x+12& = &10+7-x \\\Leftrightarrow & 6x \color{red}{+12} & = &17 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 6x+x& = &17-12 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)