Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 420x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{595} x& = & 99 \\\Leftrightarrow & x = \frac{99}{595} & & \\ & V = \left\{ \frac{99}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & -2x+\frac{10}{11} \\\Leftrightarrow & -28x-\frac{14}{5}& = & -2x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{-154} & = & \color{red}{-110x} +50 \\\Leftrightarrow & -1540x \color{red}{-154} \color{blue}{+154} \color{blue}{+110x} & = & \color{red}{-110x} +50 \color{blue}{+110x} \color{blue}{+154} \\\Leftrightarrow & -1540x+110x& = & 50+154 \\\Leftrightarrow & \color{red}{-1430} x& = & 204 \\\Leftrightarrow & x = \frac{204}{-1430} & & \\\Leftrightarrow & x = \frac{-102}{715} & & \\ & V = \left\{ \frac{-102}{715} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{11})& = & 6x+\frac{6}{5} \\\Leftrightarrow & 35x+\frac{28}{11}& = & 6x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x+ \frac{140}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{+140} & = & \color{red}{330x} +66 \\\Leftrightarrow & 1925x \color{red}{+140} \color{blue}{-140} \color{blue}{-330x} & = & \color{red}{330x} +66 \color{blue}{-330x} \color{blue}{-140} \\\Leftrightarrow & 1925x-330x& = & 66-140 \\\Leftrightarrow & \color{red}{1595} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{1595} & & \\ & V = \left\{ \frac{-74}{1595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -16x+\frac{20}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+220} & = & \color{red}{539x} +14 \\\Leftrightarrow & -1232x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & -1232x-539x& = & 14-220 \\\Leftrightarrow & \color{red}{-1771} x& = & -206 \\\Leftrightarrow & x = \frac{-206}{-1771} & & \\\Leftrightarrow & x = \frac{206}{1771} & & \\ & V = \left\{ \frac{206}{1771} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+24} & = & \color{red}{-77x} +10 \\\Leftrightarrow & 198x \color{red}{+24} \color{blue}{-24} \color{blue}{+77x} & = & \color{red}{-77x} +10 \color{blue}{+77x} \color{blue}{-24} \\\Leftrightarrow & 198x+77x& = & 10-24 \\\Leftrightarrow & \color{red}{275} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{275} & & \\ & V = \left\{ \frac{-14}{275} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & -8x+\frac{7}{9} \\\Leftrightarrow & 9x-\frac{6}{11}& = & -8x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{891}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 891x \color{red}{-54} & = & \color{red}{-792x} +77 \\\Leftrightarrow & 891x \color{red}{-54} \color{blue}{+54} \color{blue}{+792x} & = & \color{red}{-792x} +77 \color{blue}{+792x} \color{blue}{+54} \\\Leftrightarrow & 891x+792x& = & 77+54 \\\Leftrightarrow & \color{red}{1683} x& = & 131 \\\Leftrightarrow & x = \frac{131}{1683} & & \\ & V = \left\{ \frac{131}{1683} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{3})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+160} & = & \color{red}{-120x} +21 \\\Leftrightarrow & 288x \color{red}{+160} \color{blue}{-160} \color{blue}{+120x} & = & \color{red}{-120x} +21 \color{blue}{+120x} \color{blue}{-160} \\\Leftrightarrow & 288x+120x& = & 21-160 \\\Leftrightarrow & \color{red}{408} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{408} & & \\ & V = \left\{ \frac{-139}{408} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+54} & = & \color{red}{-165x} +22 \\\Leftrightarrow & -396x \color{red}{+54} \color{blue}{-54} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-54} \\\Leftrightarrow & -396x+165x& = & 22-54 \\\Leftrightarrow & \color{red}{-231} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-231} & & \\\Leftrightarrow & x = \frac{32}{231} & & \\ & V = \left\{ \frac{32}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{11})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 24x-\frac{24}{11}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{165x} +77 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{-165x} & = & \color{red}{165x} +77 \color{blue}{-165x} \color{blue}{+72} \\\Leftrightarrow & 792x-165x& = & 77+72 \\\Leftrightarrow & \color{red}{627} x& = & 149 \\\Leftrightarrow & x = \frac{149}{627} & & \\ & V = \left\{ \frac{149}{627} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & -3x+\frac{5}{7} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-112} & = & \color{red}{-231x} +55 \\\Leftrightarrow & -616x \color{red}{-112} \color{blue}{+112} \color{blue}{+231x} & = & \color{red}{-231x} +55 \color{blue}{+231x} \color{blue}{+112} \\\Leftrightarrow & -616x+231x& = & 55+112 \\\Leftrightarrow & \color{red}{-385} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-385} & & \\\Leftrightarrow & x = \frac{-167}{385} & & \\ & V = \left\{ \frac{-167}{385} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{11})& = & 2x+\frac{8}{5} \\\Leftrightarrow & 9x-\frac{15}{11}& = & 2x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-75} & = & \color{red}{110x} +88 \\\Leftrightarrow & 495x \color{red}{-75} \color{blue}{+75} \color{blue}{-110x} & = & \color{red}{110x} +88 \color{blue}{-110x} \color{blue}{+75} \\\Leftrightarrow & 495x-110x& = & 88+75 \\\Leftrightarrow & \color{red}{385} x& = & 163 \\\Leftrightarrow & x = \frac{163}{385} & & \\ & V = \left\{ \frac{163}{385} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{11})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-12} & = & \color{red}{55x} +4 \\\Leftrightarrow & -132x \color{red}{-12} \color{blue}{+12} \color{blue}{-55x} & = & \color{red}{55x} +4 \color{blue}{-55x} \color{blue}{+12} \\\Leftrightarrow & -132x-55x& = & 4+12 \\\Leftrightarrow & \color{red}{-187} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-187} & & \\\Leftrightarrow & x = \frac{-16}{187} & & \\ & V = \left\{ \frac{-16}{187} \right\} & \\\end{align}\)