Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & 7x+\frac{7}{3} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+36} & = & \color{red}{105x} +35 \\\Leftrightarrow & -450x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +35 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -450x-105x& = & 35-36 \\\Leftrightarrow & \color{red}{-555} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-555} & & \\\Leftrightarrow & x = \frac{1}{555} & & \\ & V = \left\{ \frac{1}{555} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{9})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -4x+\frac{4}{9}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{+44} & = & \color{red}{495x} +36 \\\Leftrightarrow & -396x \color{red}{+44} \color{blue}{-44} \color{blue}{-495x} & = & \color{red}{495x} +36 \color{blue}{-495x} \color{blue}{-44} \\\Leftrightarrow & -396x-495x& = & 36-44 \\\Leftrightarrow & \color{red}{-891} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-891} & & \\\Leftrightarrow & x = \frac{8}{891} & & \\ & V = \left\{ \frac{8}{891} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -4x-\frac{6}{11}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-88}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -88x \color{red}{-12} & = & \color{red}{-198x} +99 \\\Leftrightarrow & -88x \color{red}{-12} \color{blue}{+12} \color{blue}{+198x} & = & \color{red}{-198x} +99 \color{blue}{+198x} \color{blue}{+12} \\\Leftrightarrow & -88x+198x& = & 99+12 \\\Leftrightarrow & \color{red}{110} x& = & 111 \\\Leftrightarrow & x = \frac{111}{110} & & \\ & V = \left\{ \frac{111}{110} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 15x+\frac{20}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+20} & = & \color{red}{77x} +10 \\\Leftrightarrow & 165x \color{red}{+20} \color{blue}{-20} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{-20} \\\Leftrightarrow & 165x-77x& = & 10-20 \\\Leftrightarrow & \color{red}{88} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{88} & & \\\Leftrightarrow & x = \frac{-5}{44} & & \\ & V = \left\{ \frac{-5}{44} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-84} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 700x \color{red}{-84} \color{blue}{+84} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+84} \\\Leftrightarrow & 700x+105x& = & 50+84 \\\Leftrightarrow & \color{red}{805} x& = & 134 \\\Leftrightarrow & x = \frac{134}{805} & & \\ & V = \left\{ \frac{134}{805} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 6x+\frac{15}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+15} & = & \color{red}{55x} +8 \\\Leftrightarrow & 66x \color{red}{+15} \color{blue}{-15} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{-15} \\\Leftrightarrow & 66x-55x& = & 8-15 \\\Leftrightarrow & \color{red}{11} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & 8x+\frac{4}{5} \\\Leftrightarrow & -21x-\frac{14}{9}& = & 8x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-945}{ \color{blue}{45} }x- \frac{70}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -945x \color{red}{-70} & = & \color{red}{360x} +36 \\\Leftrightarrow & -945x \color{red}{-70} \color{blue}{+70} \color{blue}{-360x} & = & \color{red}{360x} +36 \color{blue}{-360x} \color{blue}{+70} \\\Leftrightarrow & -945x-360x& = & 36+70 \\\Leftrightarrow & \color{red}{-1305} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-1305} & & \\\Leftrightarrow & x = \frac{-106}{1305} & & \\ & V = \left\{ \frac{-106}{1305} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+30} & = & \color{red}{-70x} +42 \\\Leftrightarrow & 315x \color{red}{+30} \color{blue}{-30} \color{blue}{+70x} & = & \color{red}{-70x} +42 \color{blue}{+70x} \color{blue}{-30} \\\Leftrightarrow & 315x+70x& = & 42-30 \\\Leftrightarrow & \color{red}{385} x& = & 12 \\\Leftrightarrow & x = \frac{12}{385} & & \\ & V = \left\{ \frac{12}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+120} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 660x \color{red}{+120} \color{blue}{-120} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-120} \\\Leftrightarrow & 660x+275x& = & 66-120 \\\Leftrightarrow & \color{red}{935} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{935} & & \\ & V = \left\{ \frac{-54}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{-96} & = & \color{red}{-200x} +35 \\\Leftrightarrow & -480x \color{red}{-96} \color{blue}{+96} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{+96} \\\Leftrightarrow & -480x+200x& = & 35+96 \\\Leftrightarrow & \color{red}{-280} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-280} & & \\\Leftrightarrow & x = \frac{-131}{280} & & \\ & V = \left\{ \frac{-131}{280} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 700x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & 700x+245x& = & 42-50 \\\Leftrightarrow & \color{red}{945} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{945} & & \\ & V = \left\{ \frac{-8}{945} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{5})& = & -9x+\frac{3}{8} \\\Leftrightarrow & 8x+\frac{16}{5}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{320}{ \color{blue}{40} }x+ \frac{128}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 320x \color{red}{+128} & = & \color{red}{-360x} +15 \\\Leftrightarrow & 320x \color{red}{+128} \color{blue}{-128} \color{blue}{+360x} & = & \color{red}{-360x} +15 \color{blue}{+360x} \color{blue}{-128} \\\Leftrightarrow & 320x+360x& = & 15-128 \\\Leftrightarrow & \color{red}{680} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{680} & & \\ & V = \left\{ \frac{-113}{680} \right\} & \\\end{align}\)