Algebra Quiz: Class 9

Algebra Concepts and Solutions

• Solve for ( x ) in the equation ( 2x + 5 = 13 ): ( x = 4 )
• Solve for ( y ) in ( 3y - 4 = 11 ): ( y = 5 )
• The solutions of ( x^2 - 9 = 0 ) are ( x = -3 ) and ( x = 3 )
• Simplify ( 4a + 3a - 5 ): results in ( 7a - 5 )
• Solve for ( x ) in ( 2x - 7 = 5 ): ( x = 6 )
• Evaluate ( 3x + 2 ) at ( x = -1 ): yields ( -1 )

Quadratic Equations and Factorization

• Solve the quadratic equation ( x^2 + 5x + 6 = 0 ): solutions are ( x = -2 ) and ( x = -3 )
• Factor ( x^2 - 16 ): results in ( (x - 4)(x + 4) )

Additional Algebraic Solutions

• Solve ( 2x - \frac{1}{3} = 4 ): ( x = 5 )
• Simplify ( 3(x + 4) - 2x ): results in ( x + 12 )

Coefficients and Simple Equations

• In ( 7y - 2x + 3 ), the coefficient of ( y ) is ( 7 )
• Solve for ( x ) in ( x + 2 = 5 ): ( x = 3 )
• Solve ( 4(x - 2) = 12 ): ( x = 5 )

Simplifying Expressions

• Simplify ( 2x^2 + 4x ): results in ( 2x(x + 2) )
• Solve ( 5x - 2 = 3x + 6 ): ( x = 4 )
• Solve ( 3(x - 2) = 2x + 6 ): ( x = 12 )

Evaluating Expressions

• Evaluate ( 2x^2 - 3x + 4 ) at ( x = 2 ): result is ( 10 )
• Factor ( x^2 + 4x + 3 ): results in ( (x + 1)(x + 3) )

Simplifying Differences of Polynomials

• Simplify ( (3x^2 - x) - (2x^2 + x) ): results in ( x^2 - 2x )

Slope of Lines

• The slope of the line given by ( 2x - 3y = 6 ) is ( \frac{2}{3} ) when expressed in slope-intercept form.