Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x-6)& = & 7 \color{red}{-} (-4+x) \\\Leftrightarrow & -8x-12& = &7+4-x \\\Leftrightarrow & -8x \color{red}{-12} & = &11 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -8x+x& = &11+12 \\\Leftrightarrow & -7x& = &23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+6)& = & -10 \color{red}{-} (10-5x) \\\Leftrightarrow & -6x+12& = &-10-10+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-20 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &-20-12 \\\Leftrightarrow & -11x& = &-32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-4)& = & 13 \color{red}{-} (1+x) \\\Leftrightarrow & -4x-16& = &13-1-x \\\Leftrightarrow & -4x \color{red}{-16} & = &12 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -4x+x& = &12+16 \\\Leftrightarrow & -3x& = &28 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{28}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-28}{3} & & \\ & V = \left\{ \frac{-28}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (3x+6)& = & 10 \color{red}{-} (-13-5x) \\\Leftrightarrow & 6x+12& = &10+13+5x \\\Leftrightarrow & 6x \color{red}{+12} & = &23 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &23 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 6x-5x& = &23-12 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x-5)& = & -15 \color{red}{-} (3-5x) \\\Leftrightarrow & -6x-15& = &-15-3+5x \\\Leftrightarrow & -6x \color{red}{-15} & = &-18 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -6x-5x& = &-18+15 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-6)& = & 12 \color{red}{+} (13+x) \\\Leftrightarrow & 18x-18& = &12+13+x \\\Leftrightarrow & 18x \color{red}{-18} & = &25 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &25+18 \\\Leftrightarrow & 17x& = &43 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{43}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{43}{17} & & \\ & V = \left\{ \frac{43}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+6)& = & -13 \color{red}{-} (-9+4x) \\\Leftrightarrow & -5x+30& = &-13+9-4x \\\Leftrightarrow & -5x \color{red}{+30} & = &-4 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & -5x+4x& = &-4-30 \\\Leftrightarrow & -x& = &-34 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-34}{ \color{red}{-1} } \\\Leftrightarrow & x = 34 & & \\ & V = \left\{ 34 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x+1)& = & 14 \color{red}{-} (-14-3x) \\\Leftrightarrow & 16x+4& = &14+14+3x \\\Leftrightarrow & 16x \color{red}{+4} & = &28 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &28 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 16x-3x& = &28-4 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x+4)& = & 13 \color{red}{+} (3+x) \\\Leftrightarrow & -12x+16& = &13+3+x \\\Leftrightarrow & -12x \color{red}{+16} & = &16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -12x-x& = &16-16 \\\Leftrightarrow & -13x& = &0 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{0}{ \color{red}{-13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+6)& = & 2 \color{red}{+} (1-5x) \\\Leftrightarrow & -36x+36& = &2+1-5x \\\Leftrightarrow & -36x \color{red}{+36} & = &3 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -36x+5x& = &3-36 \\\Leftrightarrow & -31x& = &-33 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-33}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{33}{31} & & \\ & V = \left\{ \frac{33}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-7)& = & -7 \color{red}{-} (10+x) \\\Leftrightarrow & 18x-21& = &-7-10-x \\\Leftrightarrow & 18x \color{red}{-21} & = &-17 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 18x+x& = &-17+21 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-2)& = & -13 \color{red}{-} (-3+x) \\\Leftrightarrow & -30x-10& = &-13+3-x \\\Leftrightarrow & -30x \color{red}{-10} & = &-10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -30x+x& = &-10+10 \\\Leftrightarrow & -29x& = &0 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{0}{ \color{red}{-29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)