Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x+5)& = & -1 \color{red}{+} (-5+x) \\\Leftrightarrow & 30x+30& = &-1-5+x \\\Leftrightarrow & 30x \color{red}{+30} & = &-6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &-6-30 \\\Leftrightarrow & 29x& = &-36 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-36}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-36}{29} & & \\ & V = \left\{ \frac{-36}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x+7)& = & 15 \color{red}{+} (-13-3x) \\\Leftrightarrow & -16x+28& = &15-13-3x \\\Leftrightarrow & -16x \color{red}{+28} & = &2 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & -16x+3x& = &2-28 \\\Leftrightarrow & -13x& = &-26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-26}{ \color{red}{-13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x-6)& = & -6 \color{red}{-} (9+x) \\\Leftrightarrow & 16x-24& = &-6-9-x \\\Leftrightarrow & 16x \color{red}{-24} & = &-15 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 16x+x& = &-15+24 \\\Leftrightarrow & 17x& = &9 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{9}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{9}{17} & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+7)& = & 9 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+28& = &9+10-x \\\Leftrightarrow & -12x \color{red}{+28} & = &19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &19-28 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x-6)& = & -6 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x-12& = &-6-9+x \\\Leftrightarrow & -12x \color{red}{-12} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &-15+12 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x+6)& = & -12 \color{red}{-} (4+x) \\\Leftrightarrow & 4x+24& = &-12-4-x \\\Leftrightarrow & 4x \color{red}{+24} & = &-16 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 4x+x& = &-16-24 \\\Leftrightarrow & 5x& = &-40 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-40}{ \color{red}{5} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+6)& = & 15 \color{red}{-} (7+3x) \\\Leftrightarrow & -4x+12& = &15-7-3x \\\Leftrightarrow & -4x \color{red}{+12} & = &8 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -4x+3x& = &8-12 \\\Leftrightarrow & -x& = &-4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-4}{ \color{red}{-1} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-1)& = & -10 \color{red}{+} (-2+x) \\\Leftrightarrow & 20x-4& = &-10-2+x \\\Leftrightarrow & 20x \color{red}{-4} & = &-12 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 20x-x& = &-12+4 \\\Leftrightarrow & 19x& = &-8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+4)& = & 6 \color{red}{+} (-10+x) \\\Leftrightarrow & -2x+8& = &6-10+x \\\Leftrightarrow & -2x \color{red}{+8} & = &-4 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -2x-x& = &-4-8 \\\Leftrightarrow & -3x& = &-12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-12}{ \color{red}{-3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x-6)& = & 8 \color{red}{-} (1+x) \\\Leftrightarrow & -6x-36& = &8-1-x \\\Leftrightarrow & -6x \color{red}{-36} & = &7 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -6x+x& = &7+36 \\\Leftrightarrow & -5x& = &43 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{43}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-43}{5} & & \\ & V = \left\{ \frac{-43}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-6)& = & -7 \color{red}{+} (-12+x) \\\Leftrightarrow & 15x-18& = &-7-12+x \\\Leftrightarrow & 15x \color{red}{-18} & = &-19 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 15x-x& = &-19+18 \\\Leftrightarrow & 14x& = &-1 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-1}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-1}{14} & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x-3)& = & 6 \color{red}{-} (4-2x) \\\Leftrightarrow & -15x-9& = &6-4+2x \\\Leftrightarrow & -15x \color{red}{-9} & = &2 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -15x-2x& = &2+9 \\\Leftrightarrow & -17x& = &11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)