Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{5})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 21x+\frac{14}{5}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{+28} & = & \color{red}{-20x} +15 \\\Leftrightarrow & 210x \color{red}{+28} \color{blue}{-28} \color{blue}{+20x} & = & \color{red}{-20x} +15 \color{blue}{+20x} \color{blue}{-28} \\\Leftrightarrow & 210x+20x& = & 15-28 \\\Leftrightarrow & \color{red}{230} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{230} & & \\ & V = \left\{ \frac{-13}{230} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{3})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -16x-\frac{16}{3}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{48}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-48} & = & \color{red}{-63x} +8 \\\Leftrightarrow & -144x \color{red}{-48} \color{blue}{+48} \color{blue}{+63x} & = & \color{red}{-63x} +8 \color{blue}{+63x} \color{blue}{+48} \\\Leftrightarrow & -144x+63x& = & 8+48 \\\Leftrightarrow & \color{red}{-81} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-81} & & \\\Leftrightarrow & x = \frac{-56}{81} & & \\ & V = \left\{ \frac{-56}{81} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{11})& = & 2x+\frac{9}{10} \\\Leftrightarrow & 25x+\frac{10}{11}& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2750}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{220}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2750x \color{red}{+100} & = & \color{red}{220x} +99 \\\Leftrightarrow & 2750x \color{red}{+100} \color{blue}{-100} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{-100} \\\Leftrightarrow & 2750x-220x& = & 99-100 \\\Leftrightarrow & \color{red}{2530} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{2530} & & \\ & V = \left\{ \frac{-1}{2530} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 20x-\frac{12}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-84} & = & \color{red}{-539x} +88 \\\Leftrightarrow & 1540x \color{red}{-84} \color{blue}{+84} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{+84} \\\Leftrightarrow & 1540x+539x& = & 88+84 \\\Leftrightarrow & \color{red}{2079} x& = & 172 \\\Leftrightarrow & x = \frac{172}{2079} & & \\ & V = \left\{ \frac{172}{2079} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -9x+\frac{6}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+66} & = & \color{red}{275x} +50 \\\Leftrightarrow & -495x \color{red}{+66} \color{blue}{-66} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-66} \\\Leftrightarrow & -495x-275x& = & 50-66 \\\Leftrightarrow & \color{red}{-770} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-770} & & \\\Leftrightarrow & x = \frac{8}{385} & & \\ & V = \left\{ \frac{8}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{20}{3}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+100} & = & \color{red}{75x} +24 \\\Leftrightarrow & 180x \color{red}{+100} \color{blue}{-100} \color{blue}{-75x} & = & \color{red}{75x} +24 \color{blue}{-75x} \color{blue}{-100} \\\Leftrightarrow & 180x-75x& = & 24-100 \\\Leftrightarrow & \color{red}{105} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{105} & & \\ & V = \left\{ \frac{-76}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 24x+\frac{12}{11}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+60} & = & \color{red}{-385x} +77 \\\Leftrightarrow & 1320x \color{red}{+60} \color{blue}{-60} \color{blue}{+385x} & = & \color{red}{-385x} +77 \color{blue}{+385x} \color{blue}{-60} \\\Leftrightarrow & 1320x+385x& = & 77-60 \\\Leftrightarrow & \color{red}{1705} x& = & 17 \\\Leftrightarrow & x = \frac{17}{1705} & & \\ & V = \left\{ \frac{17}{1705} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{-245x} +40 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +40 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 210x+245x& = & 40+84 \\\Leftrightarrow & \color{red}{455} x& = & 124 \\\Leftrightarrow & x = \frac{124}{455} & & \\ & V = \left\{ \frac{124}{455} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{-42x} +27 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & 120x+42x& = & 27-40 \\\Leftrightarrow & \color{red}{162} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{162} & & \\ & V = \left\{ \frac{-13}{162} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 9x+\frac{9}{10} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-75} & = & \color{red}{180x} +18 \\\Leftrightarrow & -400x \color{red}{-75} \color{blue}{+75} \color{blue}{-180x} & = & \color{red}{180x} +18 \color{blue}{-180x} \color{blue}{+75} \\\Leftrightarrow & -400x-180x& = & 18+75 \\\Leftrightarrow & \color{red}{-580} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-580} & & \\\Leftrightarrow & x = \frac{-93}{580} & & \\ & V = \left\{ \frac{-93}{580} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{3}{7} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{-98} & = & \color{red}{-168x} +9 \\\Leftrightarrow & -441x \color{red}{-98} \color{blue}{+98} \color{blue}{+168x} & = & \color{red}{-168x} +9 \color{blue}{+168x} \color{blue}{+98} \\\Leftrightarrow & -441x+168x& = & 9+98 \\\Leftrightarrow & \color{red}{-273} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-273} & & \\\Leftrightarrow & x = \frac{-107}{273} & & \\ & V = \left\{ \frac{-107}{273} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & -4x+\frac{6}{7} \\\Leftrightarrow & 15x+\frac{6}{5}& = & -4x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+42} & = & \color{red}{-140x} +30 \\\Leftrightarrow & 525x \color{red}{+42} \color{blue}{-42} \color{blue}{+140x} & = & \color{red}{-140x} +30 \color{blue}{+140x} \color{blue}{-42} \\\Leftrightarrow & 525x+140x& = & 30-42 \\\Leftrightarrow & \color{red}{665} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{665} & & \\ & V = \left\{ \frac{-12}{665} \right\} & \\\end{align}\)